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

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3158
There’s a party in town and Mike can’t decide what to wear. However  [#permalink]

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Updated on: 13 Aug 2018, 07:44
2
1
00:00

Difficulty:

25% (medium)

Question Stats:

75% (01:18) correct 25% (01:31) wrong based on 141 sessions

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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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Originally posted by EgmatQuantExpert on 04 Apr 2018, 06:34.
Last edited by EgmatQuantExpert on 13 Aug 2018, 07:44, edited 6 times in total.
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Joined: 26 Feb 2016
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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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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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Joined: 04 Jan 2015
Posts: 3158
Re: There’s a party in town and Mike can’t decide what to wear. However  [#permalink]

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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.

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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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20 Apr 2018, 09:05
2
Option C.

5 socks + "No Socks" = 6 ways.

So, 3*4*6 = 72 ways.
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Posts: 13740
Re: There’s a party in town and Mike can’t decide what to wear. However  [#permalink]

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10 Aug 2019, 02:32
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Re: There’s a party in town and Mike can’t decide what to wear. However   [#permalink] 10 Aug 2019, 02:32
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