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  • A board of directors needs to be formed with 9 members from a pool of 15 candidates. However, two specific candidates, James and Rachel, cannot be on the board together.

A board of directors needs to be formed with 9 members from a pool of 15 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

3003


Option: 2

6006


Option: 3

9006


Option: 4

8005


Answers (1)

best_answer

Number of candidates = 15

Number of board members to be selected = 9

Number of ways to select 9 board members from 15 without James and Rachel together:

Selecting James:

We need to select 8 more board members from the remaining 14 (excluding James and Rachel). This can be done in \mathrm{C(14,8)} ways.

Selecting Rachel:

Similarly, we need to select 8 more board members from the remaining 14 (excluding James and Rachel). This can also be done in \mathrm{C(14,8)}ways.

\mathrm{\text { Total number of ways }=C(14,8)+C(14,8)=3003+3003=6006 \text { ways. }}

Hence option 2 is correct.

 

 

Posted by

Ritika Kankaria

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