A party of 6 is to be formed from 10 boys and 7 girls so as to include 3 boys - Maths - Permutations and Combinations

Question

A party of 6 is to be formed from 10 boys and 7 girls so as to
include 3 boys and 3 girls In how many different ways can the party
be formed if two particular girls refuse to join the same party
?

Rajat Sethi · Accepted Answer

Let A and B be the two girls that refuse to go together
Case 1
 A is going,B is notNo of ways = C310 ×C36Case 2
B  is going,A is notNo of ways = C310 ×C36Case 3
 Both A and B are not going
No of ways =C310 ×C35Total ways = C310 ( C36 + C36 +C35 )

A party of 6 is to be formed from 10 boys and 7 girls so as to include 3 boys and 3 girls. In how many different ways can the party be formed if two particular girls refuse to join the same party ?