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QOTD #4 The number of distinct ways to

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QOTD #4 The number of distinct ways to [#permalink] New post 02 Jul 2016, 06:47
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Question Stats:

77% (00:49) correct 22% (00:46) wrong based on 31 sessions
Quantity A
Quantity B
The number of distinct ways to form a line of 3 people by choosing from 6 people, where order matters
The number of distinct ways to form a line
of 3 people by choosing from 10 people, where order does not matter


A Quantity A is greater.
B Quantity B is greater.
C The two quantities are equal.
D The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: QOTD #4 The number of distinct ways to [#permalink] New post 04 Jul 2016, 21:07
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Choice A: 6*5*4 = 120 ways

Choice B: (10*9*8)/(1*2*3) = 120 ways;

Hence answer C
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Re: QOTD #4 The number of distinct ways to [#permalink] New post 04 Apr 2018, 02:17
Hi! Can you explain why you divide (10*9*8)/ (1*2*3)? Is it anything related to “the order doesn’t not matter”?
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Re: QOTD #4 The number of distinct ways to [#permalink] New post 04 Apr 2018, 06:24
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Quantity A: When order doesn't matter, we have to select 3 out of 6 people and can arrange those 3. Selecting 3 out of 6 people is 6C3 and then arranging three people in a row would be 3!.
So, A = 6C3 * 3! = 6*5*4 = 120

Another way of doing this is that suppose we have three positions to be filled. The first position can be filled in 6 ways, second can be filled in 5 ways and third in 4 ways. And since these have to happen together, we would take the product of 6, 5 and 4. So Quantity A would be 6*5*4 =120

Quantity 2:
Simply selecting 3 people out of 10 i.e. 10C3 = 120.

Hence Quantity A equals B
Re: QOTD #4 The number of distinct ways to   [#permalink] 04 Apr 2018, 06:24
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QOTD #4 The number of distinct ways to

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