GMAT Changed on April 16th - Read about the latest changes here

 It is currently 25 Apr 2018, 07:35

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Cody, an avid basketball player, will always wear one or more of the

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 44655
Cody, an avid basketball player, will always wear one or more of the [#permalink]

### Show Tags

25 Dec 2017, 01:37
00:00

Difficulty:

25% (medium)

Question Stats:

59% (01:03) correct 41% (00:52) wrong based on 33 sessions

### HideShow timer Statistics

Cody, an avid basketball player, will always wear one or more of the following articles of "lucky" clothing to play basketball: an old sweatband, a pair of black tube socks, an old jersey, or his mother's basketball shorts. If Cody is getting dressed to play basketball, how many different combinations of these articles of clothing are possible? (Assume the order of the clothing does not matter.)

A. 256
B. 24
C. 15
D. 12
E. 4
[Reveal] Spoiler: OA

_________________
examPAL Representative
Joined: 07 Dec 2017
Posts: 305
Re: Cody, an avid basketball player, will always wear one or more of the [#permalink]

### Show Tags

25 Dec 2017, 02:20
Bunuel wrote:
Cody, an avid basketball player, will always wear one or more of the following articles of "lucky" clothing to play basketball: an old sweatband, a pair of black tube socks, an old jersey, or his mother's basketball shorts. If Cody is getting dressed to play basketball, how many different combinations of these articles of clothing are possible? (Assume the order of the clothing does not matter.)

A. 256
B. 24
C. 15
D. 12
E. 4

The difficulty of combinatorial questions is usually in understanding how to do the calculation.
This requires an understanding of the underlying logic, e.g a Logical approach.

Cody has 4 items of clothing and he must choose at least 1 of them.
The simplest way to solve this question is to look at each item of clothing separately and ask 'Will Cody take it?'
That is - he can take or not take the sweatband - 2 options.
He can take or not take the socks - 2 options.
He can take or not take the jersey - 2 options and the same for the shorts - 2 options.
Each of these decisions is independent so multiplying all our options we hav 2*2*2*2 = 16 options.
Since Cody must take at least one item then the option where he takes nothing is impossible so there a total of 16 - 1 = 15 options.

**A different solution would be to just brute force list all the options.
This works because there are only 4 items so there aren't too many different choices.
This approach is very good to avoid wasting time if you tend to get stuck on abstract questions.
_________________

David
Senior tutor at examPAL
Signup for a free GMAT course

We won some awards:

Save up to \$250 on examPAL packages (special for GMAT Club members)

VP
Joined: 28 Mar 2017
Posts: 1001
Location: India
Concentration: Finance, Technology
GMAT 1: 730 Q49 V41
GPA: 4
Cody, an avid basketball player, will always wear one or more of the [#permalink]

### Show Tags

25 Dec 2017, 04:00
Bunuel wrote:
Cody, an avid basketball player, will always wear one or more of the following articles of "lucky" clothing to play basketball: an old sweatband, a pair of black tube socks, an old jersey, or his mother's basketball shorts. If Cody is getting dressed to play basketball, how many different combinations of these articles of clothing are possible? (Assume the order of the clothing does not matter.)

A. 256
B. 24
C. 15
D. 12
E. 4

We have 4 items and Cody wears atleast one of them. Thus possible combinations are as follows:
$$4C4$$ + $$4C3$$ + $$4C2$$ + $$4C1$$ = 1+4+6+4 =15
_________________

Kudos if my post helps!

Long And A Fruitful Journey - V21 to V41; If I can, So Can You!!

My study resources:
1. Useful Formulae, Concepts and Tricks-Quant
2. e-GMAT's ALL SC Compilation
3. LSAT RC compilation
4. Actual LSAT CR collection by Broal
5. QOTD RC (Carcass)
6. Challange OG RC
7. GMAT Prep Challenge RC

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 1029
Re: Cody, an avid basketball player, will always wear one or more of the [#permalink]

### Show Tags

25 Dec 2017, 05:37

Solution

Given :
• Cody can wear one or more of the following articles :
o Old Seatband
o Pair of Black Tube Socks
o Old Jersey

Find:

• We need to find, in how many ways can he get dressed to play basketball.

Approach:

• There are four possible cases:
o Cody wears only one article: 4C1 = 4
o Cody wears two articles: 4C2 = 6
o Cody wears three articles = 4C3 = 4
o Cody wears all the four articles = 4C4 = 1
• Thus, total ways in which Cody can dressed to play basketball = 4 + 6 + 4 + 1 = 15 ways

Thus, the correct answer is Option C.

Thanks,
Saquib
Quant Expert
e-GMAT
_________________

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 1029
Re: Cody, an avid basketball player, will always wear one or more of the [#permalink]

### Show Tags

25 Dec 2017, 05:39

Method 2:

Approach:

While choosing any of the articles, there are two possibilities :
• Either Cody will choose the article OR
• He will not choose to wear it.

o Thus, we can conclude that there are two ways in which an articles may be selected or not selected.

• While dressing up, he may choose or not choose to wear the old seatband in 2 ways
• While dressing up, he may choose or not choose to wear the Pair of Black Tube Socks in 2 ways
• While dressing up, he may choose or not choose to wear the old jersey in 2 ways
• While dressing up, he may choose or not choose to wear the basket ball in 2 ways

o Thus, the total ways to select or not select the 4 items = 2 * 2 * 2 * 2 = 16
o Note: There is only one way in which we do not select any of the items and we need to remove that case from the total cases, because Cody is going to wear atleast one or more of the articles.

• Thus, the total number of ways in which Cody can get dressed to play basketball = 16 – 1 = 15 ways.

Thus, the correct answer is Option C.
_________________

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Re: Cody, an avid basketball player, will always wear one or more of the   [#permalink] 25 Dec 2017, 05:39
Display posts from previous: Sort by