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  • A committee of 7 people needs to be formed from a group of 10 individuals. However, two specific individuals, David and Emma, cannot be on the committee together. In how

A committee of 7 people needs to be formed from a group of 10 individuals. However, two specific individuals, David and Emma, cannot be on the committee together. In how many ways can the committee be formed?

Option: 1

56


Option: 2

96


Option: 3

16


Option: 4

36


Answers (1)

best_answer

Number of individuals = 10

Number of committee members to be selected = 7

Number of ways to select 7 members from 10 without David and Emma together:

Selecting David:

We need to select 6 more members from the remaining 8 (excluding David and Emma). This can be done in \mathrm{C(8,6)} ways.

Selecting Emma:

Similarly, we need to select 6 more members from the remaining 8 (excluding David and Emma). This can also be done in \mathrm{C(8,6)} ways.

\mathrm{\text { Total number of ways }=C(8,6)+C(8,6)=28+28=56 \text { ways. }}

Hence option 1 is correct.

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