Prove that n!(n + 2) = n! + (n + 1)!

Out of 18 points in a plane, no three are in the same line except five points which are collinear. Find the number of lines that can be formed joining the points.

A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of exactly 3 girls

A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: almost 3 girls?

3²ⁿ - 1 is divisible by 8