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  • A committee of 5 members needs to be formed from a group of 10 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 10 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

652


Option: 2

854


Option: 3

196


Option: 4

228


Answers (1)

best_answer

Number of professionals = 10

Number of professionals to be selected = 5

Number of ways to select 5 professionals from 10 without Michael and Lisa together:

Total number of ways to form the committee without any restrictions \mathrm{= C(10,5)}

Number of ways Michael and Lisa are together \mathrm{= C(8,3)}

Number of ways committee can be formed with Michael and Lisa together = Total number of ways - Number of ways Michael and Lisa are together \mathrm{= C(10,5)-C(8,3)}

\mathrm{\text{Number of ways committee can be formed }= C(10,5)-C(8,3)=252-56=196ways.}

Hence option 3 is correct.

 

 

Posted by

Ajit Kumar Dubey

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