GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 21 Oct 2019, 18:33

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Out of 5 boys and 6 girls, 4 students are sellected at rando

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Manager
Manager
User avatar
S
Joined: 20 Jul 2018
Posts: 87
GPA: 2.87
Out of 5 boys and 6 girls, 4 students are sellected at rando  [#permalink]

Show Tags

New post 25 Aug 2018, 02:03
1
6
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

64% (02:40) correct 36% (02:45) wrong based on 78 sessions

HideShow timer Statistics

Out of 5 boys and 6 girls, 4 students are selected at random, what is the probability that selection has more number of girls than the number of boys?

\(A) \frac{1}{33}\)
\(B) \frac{15}{33}\)
\(C) \frac{23}{66}\)
\(D) \frac{12}{33}\)
\(E) \frac{1}{3}\)

Posted from my mobile device

_________________
Hasnain Afzal

"When you wanna succeed as bad as you wanna breathe, then you will be successful." -Eric Thomas
Senior Manager
Senior Manager
User avatar
V
Joined: 22 Feb 2018
Posts: 419
Out of 5 boys and 6 girls, 4 students are sellected at rando  [#permalink]

Show Tags

New post 25 Aug 2018, 02:24
2
hasnain3047 wrote:
Out of 5 boys and 6 girls, 4 students are selected at random, what is the probability that selection has more number of girls than the number of boys?

\(A) \frac{1}{33}\)
\(B) \frac{15}{33}\)
\(C) \frac{23}{66}\)
\(D) \frac{12}{33}\)
\(E) \frac{1}{3}\)

Posted from my mobile device


OA: C

Total Number of case of selecting four students out of 11 \(= C(11,4) = \frac{11!}{7!4!}=330\)

Number of ways of selecting 4 girls or 3 girls and 1 boy to form a 4 member team \(= C(6,4)*1 + C(6,3)*C(5,1)=\frac{6!}{4!2!}*1 +\frac{6!}{3!3!}*\frac{5!}{4!1!}=115\)

Required probability \(= \frac{115}{330} =\frac{23}{66}\)
_________________
Good, good Let the kudos flow through you
e-GMAT Representative
User avatar
V
Joined: 04 Jan 2015
Posts: 3078
Re: Out of 5 boys and 6 girls, 4 students are sellected at rando  [#permalink]

Show Tags

New post 25 Aug 2018, 02:30
2

Solution



Given:
    • Out of 5 boys and 6 girls, 4 students are selected at random.

To find:
    • The probability that selection has more number of girls than the number of boys.

Approach and Working:
From 11 students, 4 can be selected in \(^{11}C_4\) = 330 ways

Now, if number of girls are more than boys, then the possible cases are:
    • 3 girls and 1 boy = \(^6C_3\) x \(^5C_1\) = 20 x 5 = 100
    • 4 girls and 0 boy = \(^6C_4\) = 15
    • Hence, the probability = \(\frac{100+15}{330} = \frac{115}{330} = \frac{23}{66}\)

Hence, the correct answer is option C.

Answer: C

Image

_________________
Director
Director
User avatar
G
Joined: 20 Feb 2015
Posts: 762
Concentration: Strategy, General Management
Out of 5 boys and 6 girls, 4 students are sellected at rando  [#permalink]

Show Tags

New post 28 Aug 2018, 01:32
hasnain3047 wrote:
Out of 5 boys and 6 girls, 4 students are selected at random, what is the probability that selection has more number of girls than the number of boys?

\(A) \frac{1}{33}\)
\(B) \frac{15}{33}\)
\(C) \frac{23}{66}\)
\(D) \frac{12}{33}\)
\(E) \frac{1}{3}\)

Posted from my mobile device



more number of girls than boys is possible in 2 cases

1. 3 girls and 1 boy = \(\frac{6c3*5}{11c4}\)
2. all 4 girls = \(\frac{6c4}{11c4}\)

= \(\frac{115}{330}\) =\(\frac{23}{66}\)
GMAT Club Bot
Out of 5 boys and 6 girls, 4 students are sellected at rando   [#permalink] 28 Aug 2018, 01:32
Display posts from previous: Sort by

Out of 5 boys and 6 girls, 4 students are sellected at rando

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne