Nusa84 wrote:

In a class of 10 students, a group of 4 will be selected for a trip. How many different groups are possible, if 2 of those 10 students are a married couple and will only travel together?

Answers:

A. 98

B. 115

C. 122

D. 126

E. 165

I keep getting the wrong answer all the time ...

Thanks

We can have either two married students plus two other students or 4 students out of 8 (no married student among them).

\(C^1_1*C^2_{8}+C^4_{8}=28+70=98\).

\(C^1_1\) - # of ways to choose 1 couple out of 1 couple;

\(C^2_{8}\) - # of ways to choose 2 students out of 8 left (10 - 2 married=8);

\(C^4_{8}\) - # of ways to choose 4 student out of 8 (so not to choose any married student).

Answer: A.

Hope it's clear.

Yes it is, sometimes i get very stuck with these questions. Thanks!