Bunuel 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
There are two scenarios
Case 1: When Alice and David are in group of 7 : Total ways to make such groups of 7 and 3 = 8C5 (To select 5 more out of 8 to make group of 7 which includes Alice and David already)
This way the other group of 3 is automatically formed, 8C5 = 56
Case 2: When Alice and David are in group of 3 : Total ways to make such groups of 3 and 7 = 8C1 (To select 1 more out of 8 to make group of 3 which includes Alice and David already)
This way the other group of 7 is automatically formed, 8C1 = 8
Total Possible ways = 56+8 = 64
Answer: Option C
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