Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 18 Jul 2019, 01:59

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# A class consists of 5 boys and 4 girls. Given that one kid can only ho

Author Message
TAGS:

### Hide Tags

Retired Moderator
Joined: 29 Apr 2015
Posts: 830
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
A class consists of 5 boys and 4 girls. Given that one kid can only ho  [#permalink]

### Show Tags

06 Jul 2015, 10:31
2
10
00:00

Difficulty:

55% (hard)

Question Stats:

55% (01:43) correct 45% (01:31) wrong based on 272 sessions

### HideShow timer Statistics

A class consists of 5 boys and 4 girls. Given that one kid can only hold one title, in how many ways can you pick 2 boys to be the class clown and the teacher's pet or 2 girls to be the most beautiful girl in class and the smartest kid on the block?

A. 9
B. 18
C. 32
D. 60
E. 240

_________________
Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.
Intern
Joined: 04 Jul 2015
Posts: 3
Re: A class consists of 5 boys and 4 girls. Given that one kid can only ho  [#permalink]

### Show Tags

14 Jul 2015, 14:07
(5c2 * 2!) + (4c2 * 2!)
Senior Manager
Joined: 28 Jun 2015
Posts: 286
Concentration: Finance
GPA: 3.5
Re: A class consists of 5 boys and 4 girls. Given that one kid can only ho  [#permalink]

### Show Tags

14 Jul 2015, 18:20
Number of ways of choosing 2 boys out of 5 boys = 5C2.
Number of ways of choosing 2 girs out of 4 girls = 4C2.

The chosen boy/girl can hold any of the two respective titles, so total number of ways = (5C2 * 2!) + (4C2 * 2!) = 20 + 12 = 32 ways. Ans (C).
_________________
I used to think the brain was the most important organ. Then I thought, look what’s telling me that.
CEO
Joined: 20 Mar 2014
Posts: 2620
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: A class consists of 5 boys and 4 girls. Given that one kid can only ho  [#permalink]

### Show Tags

14 Jul 2015, 18:34
1
reto wrote:
A class consists of 5 boys and 4 girls. Given that one kid can only hold one title, in how many ways can you pick 2 boys to be the class clown and the teacher's pet or 2 girls to be the most beautiful girl in class and the smartest kid on the block?

A. 9
B. 18
C. 32
D. 60
E. 240

Easiest way is to treat it like an arrangements question in the following manner:

From the boys we need to select 2 to be clown and pet: This can be done in 5*4 ways

Similarly for the girls, we have 4*3 ways.

Thus total = 20+12 = 32 ways. Thus C is the correct answer.
Manager
Joined: 29 May 2013
Posts: 100
Location: India
Concentration: Technology, Marketing
WE: Information Technology (Consulting)
Re: A class consists of 5 boys and 4 girls. Given that one kid can only ho  [#permalink]

### Show Tags

14 Jul 2015, 22:48
hey can somebody please explain when to add combinations and when to mulitply combinations?
Senior Manager
Joined: 28 Jun 2015
Posts: 286
Concentration: Finance
GPA: 3.5
A class consists of 5 boys and 4 girls. Given that one kid can only ho  [#permalink]

### Show Tags

14 Jul 2015, 22:51
1
Hi jayanthjanardhan,

the combinations are to be multiplied when there is an AND (intersection of two sets/events) and added when there is an OR (union).
_________________
I used to think the brain was the most important organ. Then I thought, look what’s telling me that.
Manager
Joined: 29 May 2013
Posts: 100
Location: India
Concentration: Technology, Marketing
WE: Information Technology (Consulting)
Re: A class consists of 5 boys and 4 girls. Given that one kid can only ho  [#permalink]

### Show Tags

15 Jul 2015, 01:06
i get it now!...thanks FireStorm!
Intern
Joined: 13 Jan 2011
Posts: 22
Re: A class consists of 5 boys and 4 girls. Given that one kid can only ho  [#permalink]

### Show Tags

28 Sep 2015, 04:45
Why does the order matter?
CEO
Joined: 20 Mar 2014
Posts: 2620
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: A class consists of 5 boys and 4 girls. Given that one kid can only ho  [#permalink]

### Show Tags

28 Sep 2015, 04:49
dor1209 wrote:
Why does the order matter?

Because you have 2 distinct titles to give.

Let's say you have 2 kids A and B and you need to award the 2 different titles to them.

If the order didn't matter, you'll say 1 possible combination but consider the following 2 different cases:

A becoming the clown with B becoming the pet is different from

A becoming the pet and B becoming the clown.

This is the reason why order matters.
Manager
Joined: 14 Jul 2014
Posts: 164
Location: United States
Schools: Duke '20 (D)
GMAT 1: 600 Q48 V27
GMAT 2: 720 Q50 V37
GPA: 3.2
Re: A class consists of 5 boys and 4 girls. Given that one kid can only ho  [#permalink]

### Show Tags

06 Jan 2016, 09:47
good one, forgot about multiplying two and ended up with 16..
Manager
Joined: 05 Dec 2016
Posts: 241
Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
Re: A class consists of 5 boys and 4 girls. Given that one kid can only ho  [#permalink]

### Show Tags

07 Mar 2017, 03:53
5C1*4C2+4C1*3C1=32 ways
Intern
Joined: 17 Jan 2016
Posts: 39
Location: India
Concentration: General Management, General Management
Re: A class consists of 5 boys and 4 girls. Given that one kid can only ho  [#permalink]

### Show Tags

07 Mar 2017, 08:37
1
1 boy can be chosen for class clown in 5C1 ways. Now there are 4 boys left and Teacher's pet can be chosen from this in 4C1 ways.
Since both these conditions must be fulfilled simultaneously so we have 5C1 X 4C1 as the no. of ways of choosing boys while fulfilling the given conditions.

1 girl can be chosen to be the most beautiful girl in class in 4C1 ways. Now there are 3 girls left and smartest kid on the block can be chosen from this in 3C1 ways.
Since both these conditions must be fulfilled simultaneously so we have 4C1 X 3C1 as the no. of ways of choosing girls while fulfilling the given conditions.

Since either of the given conditions needs to be fulfilled, the required number of ways will be 5C1X4C1 + 4C1X3C1 which is equal to 32.

Ans- C
Intern
Joined: 10 Jan 2017
Posts: 6
Re: A class consists of 5 boys and 4 girls. Given that one kid can only ho  [#permalink]

### Show Tags

09 Mar 2017, 03:59
FireStorm wrote:
Number of ways of choosing 2 boys out of 5 boys = 5C2.
Number of ways of choosing 2 girs out of 4 girls = 4C2.

The chosen boy/girl can hold any of the two respective titles, so total number of ways = (5C2 * 2!) + (4C2 * 2!) = 20 + 12 = 32 ways. Ans (C).

Can anyone explain the bolded part, why have we multiplied 5C2 and 4C2 by 2!?
Intern
Joined: 17 Jan 2016
Posts: 39
Location: India
Concentration: General Management, General Management
Re: A class consists of 5 boys and 4 girls. Given that one kid can only ho  [#permalink]

### Show Tags

09 Mar 2017, 23:28
There are 2 titles and any of the boy can take each of these titles. So for one title there are two options and any one of these 2 boys can take that spot. Hence we multiply by 2!.

Title 1 - Any one of the two boys can take this spot. No. of options is 2.
Title 2 - The remaining boy takes this spot. No. of options is 1.

Since both these options should happen simultaneously so we multiply. So 2!.

The same for the girls selection as well.

Now had there been 3 titles the same would have been multiplied by 3!. you can work out the details in the same way as explained above.
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6923
Location: United States (CA)
Re: A class consists of 5 boys and 4 girls. Given that one kid can only ho  [#permalink]

### Show Tags

15 Mar 2017, 16:21
reto wrote:
A class consists of 5 boys and 4 girls. Given that one kid can only hold one title, in how many ways can you pick 2 boys to be the class clown and the teacher's pet or 2 girls to be the most beautiful girl in class and the smartest kid on the block?

A. 9
B. 18
C. 32
D. 60
E. 240

We are given a class of 5 boys and 4 girls.

Let’s first determine how many ways 2 boys can be selected for class clown and teacher’s pet.

Suppose two of the boys are Adam and Ben, and they are selected as the class clown and the teacher’s pet. Saying Adam is the class clown and Ben is the teacher’s pet is DIFFERENT from saying Ben is the class clown and Adam is the teacher’s pet. Therefore, this is a permutation problem, since the order matters.

Since here we have 5 boys and we are selecting 2 for which order matters, the number of ways this can be done is:

5P2 = 5 x 4 = 20

Similarly, the number of ways 2 girls can be selected from 4 girls to be the most beautiful girl in class and the smartest kid on the block in which order matters is:

4P2 = 4 x 3 = 12

Thus, the number of ways to select them is 20 + 12 = 32.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern
Joined: 10 Jul 2017
Posts: 31
Schools: ISB '20
Re: A class consists of 5 boys and 4 girls. Given that one kid can only ho  [#permalink]

### Show Tags

18 Aug 2018, 21:54
A class consists of 5 boys and 4 girls. Given that one kid can only hold one title, in how many ways can you pick 2 boys to be the class clown AND the teacher's pet OR 2 girls to be the most beautiful girl in class AND the smartest kid on the block?

concept: AND = multiply ; OR = Add (therefore Class clown X Teach. pet +Mst beautiful X smartest kid
5C1 X 4C1 + 4C1 X 3C1 => 32 (answer)
Math Expert
Joined: 02 Aug 2009
Posts: 7764
Re: A class consists of 5 boys and 4 girls. Given that one kid can only ho  [#permalink]

### Show Tags

18 Aug 2018, 22:55
1
reto wrote:
A class consists of 5 boys and 4 girls. Given that one kid can only hold one title, in how many ways can you pick 2 boys to be the class clown and the teacher's pet or 2 girls to be the most beautiful girl in class and the smartest kid on the block?

A. 9
B. 18
C. 32
D. 60
E. 240

POINTS to note:-
1) OR - since we re looking at two different cases joined by OR and are not related to each other. so you have to ADD the ways of each case
2) two different titles - so ORDER matters

ways to pick 2 boys to be the class clown and the teacher's pet - 5P2=5*4=20 or
2 girls to be the most beautiful girl in class and the smartest kid on the block - 4P2 = 4*3 = 12

total = 20+12= 32

C
_________________
Manager
Joined: 19 Nov 2017
Posts: 183
Location: India
Schools: ISB
GMAT 1: 670 Q49 V32
GPA: 4
Re: A class consists of 5 boys and 4 girls. Given that one kid can only ho  [#permalink]

### Show Tags

18 Aug 2018, 23:23
Best thing would be to use permutations here instead of combinations, but actually you may use any.
We use permutations when we are concerned with the order and combination when we are not.
Here order matters, thus we can use permutation to get a straight answer, however, we may use combinations as well and then multiply by 2! to compensate for the inner arrangement.
_________________
Regards,

Vaibhav

Sky is the limit. 800 is the limit.

~GMAC
Manager
Joined: 10 Jan 2013
Posts: 243
Location: India
Concentration: General Management, Strategy
GPA: 3.95
Re: A class consists of 5 boys and 4 girls. Given that one kid can only ho  [#permalink]

### Show Tags

18 Aug 2018, 23:28
1
Though i got the answer is as 32.

The answer would be 20 ×12=240

Posted from my mobile device
Manager
Joined: 16 May 2016
Posts: 203
Location: India
Schools: ESSEC '21 (A\$)
GMAT 1: 720 Q50 V38
GPA: 3.5
WE: Analyst (Consulting)
Re: A class consists of 5 boys and 4 girls. Given that one kid can only ho  [#permalink]

### Show Tags

18 Aug 2018, 23:42
reto wrote:
A class consists of 5 boys and 4 girls. Given that one kid can only hold one title, in how many ways can you pick 2 boys to be the class clown and the teacher's pet or 2 girls to be the most beautiful girl in class and the smartest kid on the block?

A. 9
B. 18
C. 32
D. 60
E. 240

Since it is given one kid can hold only one title, it depicts that order of selection is fixed. When order is fixed we perform permutation and not combination.
2 boys as class clown and teacher's pet= 5*4
2 girls as the most beautiful and smartest= 4*3
It is given by OR condition, hence 5*4+4*3=32
Ans: C
Surely not 700 level question
_________________
Not Giving UP! Kudos if you like the question
Re: A class consists of 5 boys and 4 girls. Given that one kid can only ho   [#permalink] 18 Aug 2018, 23:42

Go to page    1   2    Next  [ 21 posts ]

Display posts from previous: Sort by