Alternative approach to selecting cousins using combinations

[chwala]

Homework Statement

see attached

Relevant Equations

combinations

My interest is on part b only.

I am seeking alternative approach to the problem. This was a tricky question i guess. Find my approach below;

$5C3×4C2${senior cousin included and junior not included}+ $5C4×4C1${ senior cousin not included, Junior cousin included}+$5C4×4C2${both NOT included}= $60+20+30=110$

Wah...this really boggled my mind a little bit...i only have the text solution, which is 110.

Kindly check my working then any other better approach would be welcome. Cheers guys!

 

[PeroK]

That looks fine. An alternative is to count the total number of committees and then subtract the number of committees that have both cousins.