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There’s a party in town and Mike can’t decide what to wear. However

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There’s a party in town and Mike can’t decide what to wear. However [#permalink]

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New post Updated on: 10 Apr 2018, 01:30
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Learn when to “Add” and “Multiply” in Permutation & Combination questions- Exercise Question #1

There’s a party in town and Mike can’t decide what to wear. However, he has decided to follow the following:
    1. He will wear tie and shoes
    2. He may or may not wear socks.
Mike has \(3\) ties, \(4\) pairs of shoes and \(5\) pairs of socks.
In how many ways can Mike dress for the party?

Options:
A) 12
B) 60
C) 72
D) 144
E) 288

Learn to use the Keyword Approach in Solving PnC question from the following article:

Learn when to “Add” and “Multiply” in Permutation & Combination questions


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[Reveal] Spoiler: OA

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Originally posted by EgmatQuantExpert on 04 Apr 2018, 06:34.
Last edited by EgmatQuantExpert on 10 Apr 2018, 01:30, edited 5 times in total.
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Re: There’s a party in town and Mike can’t decide what to wear. However [#permalink]

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New post 04 Apr 2018, 06:41
EgmatQuantExpert wrote:

Question:



There’s a party in town and Mike can’t decide what to wear. However, he has decided to follow the following:
    1. He will wear tie and shoes
    2. He may or may not wear socks.
Mike has \(3\) ties, \(4\) pairs of shoes and \(5\) pairs of socks.
In how many ways can Mike dress for the party?

Options:
    A)12
    B)60
    C)72
    D)144
    E) 288


There are two ways in which Mike can go to the party in town

1. Wears tie and shoes but no socks
There are 3*4 = 12 ways in which he can dress for the party

2. Wears tie, shoes, and socks
There are 3*4*5 = 60 ways in which he can dress for the party

Therefore, Mike could go to the party in 12+60 = 72 ways(Option C)

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Re: There’s a party in town and Mike can’t decide what to wear. However [#permalink]

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New post 08 Apr 2018, 21:24

Solution



Given:
    • Mike has 3 ties, 4 pairs of shoes and 5 pairs of socks
    • Mike can dress for the party in either one of the following ways:
      o He will wear ties and socks, OR
      o He may or may not wear socks

To find:
• We need to find the number of ways in which Mike can dress for the party.

Approach and Working:

Let us apply the learning of AND-OR keyword to solve this problem.

Mike can dress in two ways: Either he will wear tie and shoes, OR he may or may not wear the socks.

We have the keyword OR, thus
    • Total ways= Number of ways Mike will wear Tie and shoes +Number of ways Mike may or may not wear the socks
      o Number of ways Mike will wear Tie and shoes= 3*4(Usage of the keyword AND)

Number of ways Mike may or may not wear socks

Total ways = Mike will wear socks or mike will not wear the socks
    • Since the case when Mike will not wear the socks is same as the case when he wears only tie and shoes. And, this the case-1.
      o Hence, this case is not taken into consideration.
    • Thus, total ways= Ways to wear 1 tie from 3 ties AND ways to wear 1 shoes from 4 shoes AND ways to wear 1 socks from 5 pairs of socks
    • Total ways= 3*4*5= 60

Hence, Total ways in which Mike can dress for the party= 12+60= 72.

Hence, the correct answer is option C.

Answer: C

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Re: There’s a party in town and Mike can’t decide what to wear. However [#permalink]

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New post 20 Apr 2018, 09:05
Option C.

5 socks + "No Socks" = 6 ways.

So, 3*4*6 = 72 ways.
Re: There’s a party in town and Mike can’t decide what to wear. However   [#permalink] 20 Apr 2018, 09:05
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