Permutations and Combinations

Question

A brother and a sister, Ken and betty are among the 7 men and 5 women . Find how many different commitees of four could be selected so that there are two male and two female members which must include Ken or Betty but not both.Please check my  teachers workings and explain why is it like that? tq

 

Ken Not Betty : 6C1 x 4C2 = 60

Betty Not Ken : 4C1 x 5C2 = 36 

Total = 96 (Ans)

Answer 1

I believe that David (DelMar, Ca, 'where the turf meets the surf') erred in his second computation, "Betty but not Ken."

 

One more woman, i.e. 4C1  and any two men other than Ken, i.e. 6C2 = 4(15) = 60.

 

I believe that David also erred in his first computation, "Ken but not Betty."

 

One more man 6C1 & two women other than Betty, 4C2 = 6(6) = 36.

 

IN OTHER WORDS, THE LABELS on his two lines were reversed.  Total is still 96.