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Alice and David are two of the ten people in a group. In how

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Alice and David are two of the ten people in a group. In how [#permalink] New post 14 Aug 2018, 08:15
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Alice and David are two of the ten people in a group. In how many different ways can this group of 10 people be divided into a group of 7 people and a group of 3 people if Alice and David are to be in the same group?


A. 48

B. 56

C. 64

D. 80

E. 128

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[Reveal] Spoiler: OA

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Re: Alice and David are two of the ten people in a group. In how [#permalink] New post 14 Aug 2018, 23:15
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Carcass wrote:
Alice and David are two of the ten people in a group. In how many different ways can this group of 10 people be divided into a group of 7 people and a group of 3 people if Alice and David are to be in the same group?


A. 48

B. 56

C. 64

D. 80

E. 128

Kudos for R.A.E.


Let us consider the first the group of 7,

If DAvid and Alice are in this group then we need to choose only 5 out of 7 from total of 8 people(as David and Alice are considered in the group)

so we have 8C5 = 56 ways.

Now if David and Alice are in the group of 3 people then selecting the group from the total of 8 people will be = 8C1 = 8

So the total no. of ways = 56 + 8 = 64 ways
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Re: Alice and David are two of the ten people in a group. In how [#permalink] New post 15 Aug 2018, 17:48
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Consider Alice and David as a single person, and then divide the people into groups:

Number of ways = 6(Considering them as one in the group of 7)*3*2 + 7*2(Considering them as one in the group of 3)*2
= 64.
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Re: Alice and David are two of the ten people in a group. In how [#permalink] New post 18 Nov 2018, 16:07
parseltongue wrote:
Consider Alice and David as a single person, and then divide the people into groups:

Number of ways = 6(Considering them as one in the group of 7)*3*2 + 7*2(Considering them as one in the group of 3)*2
= 64.

I didn't get the reason for 3*2 and the last *2.
Re: Alice and David are two of the ten people in a group. In how   [#permalink] 18 Nov 2018, 16:07
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