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  • A committee of 5 members needs to be formed from a group of 11 professionals. However, two specific professionals, Michael and Lisa, cannot be on the committee together.

A committee of 5 members needs to be formed from a group of 11 professionals. However, two specific professionals, Michael and Lisa, cannot be on the committee together. In how many ways can the committee be formed?

Option: 1

292


Option: 2

274


Option: 3

252


Option: 4

250


Answers (1)

best_answer

Number of professionals = 11

Number of professionals to be selected = 5

Number of ways to select 5 professionals from 11 without Michael and Lisa together:

Selecting Michael:

We need to select 4 more professionals from the remaining 9 (excluding Michael and Lisa). This can be done in \mathrm{C(9,4)}ways.

Selecting Lisa:

Similarly, we need to select 4 more professionals from the remaining 9 (excluding Michael and Lisa). This can also be done in \mathrm{C(9,4)} ways.

\mathrm{\text { Total number of ways }=C(9,4)+C(9,4)=126+126=252 \text { ways. }}

Hence opton 3 is correct.

 

Posted by

Irshad Anwar

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