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

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

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New post 25 Dec 2017, 01:37
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Question Stats:

66% (01:19) correct 34% (01:44) wrong based on 39 sessions

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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

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Re: Cody, an avid basketball player, will always wear one or more of the  [#permalink]

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New post 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.
(C) is our answer.

**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.
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Cody, an avid basketball player, will always wear one or more of the  [#permalink]

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New post 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


My answer "C". Awaiting OA.

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
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Re: Cody, an avid basketball player, will always wear one or more of the  [#permalink]

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New post 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
      o Mother’s basketball shorts

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.

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Re: Cody, an avid basketball player, will always wear one or more of the  [#permalink]

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New post 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.
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