A team of 4 boys and 5 girls is to be made from a team of 7 boys and 8

We can see that the only way a team is NOT possible is if Sam makes the team, but his sister doesn’t. Therefore,

The number of ways a team can be selected = the total number of ways a team can be selected without any restrictions - the number of ways a team is selected with Sam in it but not his sister

The total number of ways a team can be selected without any restrictions is the number of ways to select 4 boys from 7 and 5 girls from 8, which is:

7C4 x 8C5 = (7 x 6 x 5 x 4)/(4 x 3 x 2 x 1) x (8 x 7 x 6 x 5 x 4)/(5 x 4 x 3 x 2 x 1) = 35 x 56 = 1960

The number of ways a team is selected with Sam in it but not his sister is:

1C1 x 6C3 x 1C0 x 7C5 = (6 x 5 x 4)/(3 x 2 x 1) x (7 x 6 x 5 x 4 x 3)/(5 x 4 x 3 x 2 x 1) = 20 x 21 = 420

Thus, the number of ways a team can be selected is 1960 - 420 = 1540.

Answer: D