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Updated on: 13 Aug 2018, 07:44
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.
Last edited by EgmatQuantExpert on 13 Aug 2018, 07:44, edited 6 times in total.
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C
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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:
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
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.
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
04 Apr 2018, 06:41
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EgmatQuantExpert
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.
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)
08 Apr 2018, 21:24
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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
