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  • A committee of 6 people needs to be formed from a group of 9 individuals. However, two specific individuals, David and Emma, cannot be on the committee together. In how m

A committee of 6 people needs to be formed from a group of 9 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

52


Option: 2

96


Option: 3

18


Option: 4

63


Answers (1)

best_answer

Number of individuals = 9

Number of committee members to be selected = 6

Number of ways to select 6 committee members from 9 without David and Emma together:

Total number of ways to form the committee without any restrictions \mathrm{=C(9,6)}

Number of ways David and Emma are together \mathrm{=C(7,5)}

Number of ways committee can be formed with David and Emma together = Total number of ways - Number of ways David and Emma are together \mathrm{=C(9,6)-C(7,5)}

Number of ways committee can be formed \mathrm{=C(9,6)-C(7,5)=84-21=63 ways}

Hence option 4 is correct.

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