Question

Tony and Maria are two star-crossed lovers trying to get on a committee of 4 people. If there are 9 people eligible for this committee, how many ways can exactly one of Tony and Maria be selected for the committee?

Answer 1

Answer:

The number of ways Tony and Maria can both be selected for the committee is 8 ways.

Step-by-step explanation:

i) Tony and Maria have to be on the committee together or not at all.

ii) Let us consider Tony and Maria as combined as one person.

 Therefore now we can say that the number of eligible people for the committee = 9 - 1 = 8.

iii) therefore the number of ways that both Tony and Maria can be selected for the committee are

 = 8C1   =  $\hspace{0.2cm}\binom{8}{1} = \frac{8!}{1! (8-1)!} = \frac{8!}{1!\times 7!} = \frac{8}{1} = \hspace{0.1cm}8 \hspace{0.1cm}ways$