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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