What is the probability of a family with six children having 3 boys and 3 girls?

each child could be either a boy or a girl ( 2 possibilities)

 there are 6 kids so there are 2^6 ways to have a child

2^6 = 64 possible ways

now for 3 boys it is a combination 6C3 = 6*5*4*3*2/(3*2*3*2) = 720/36 = 20 ways to have 3 boys

so probability = 20/64 reduces to 5/16 probability

10 * -6 - (-6) * 2 + 2^3 =

-40