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  • A board of directors needs to be formed with 8 members from a pool of 14 candidates. However, two specific candidates, James and Rachel, cannot be on the board together.

A board of directors needs to be formed with 8 members from a pool of 14 candidates. However, two specific candidates, James and Rachel, cannot be on the board together. In how many ways can the board be formed?

Option: 1

652


Option: 2

896


Option: 3

1520


Option: 4

3432


Answers (1)

best_answer

Number of candidates = 14

Number of board members to be selected = 8

Number of ways to select 8 board members from 14 without James and Rachel together:

Selecting James:

We need to select 7 more board members from the remaining 13 (excluding James and Rachel). This can be done in \mathrm{C(13,7)}ways.

Selecting Rachel:

Similarly, we need to select 7 more board members from the remaining 13 (excluding James and Rachel). This can also be done in \mathrm{C(13,7)} ways.

\mathrm{\text { Total \: number\: of\: ways =} C(13,7)+C(13,7)=1716+1716=3432 \text { ways. } }

Hence option 4 is correct.

Posted by

manish painkra

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