Question

how many ways can 3 boys be selected from 10 boys so as always to include the youngest boy?​

Answer 1

Following on from the previous answer, the formula for evaluating the expression is

10! / 7!

In the numerator, all the terms from the 7 onwards in the numerator cancel out with the same terms in the bottom, leaving us with just 10*9*8 = 720

Because the order is not significant, we divide this answer by 3!, giving us 720 /6 = 120.

The final fornula is 10!/(7!*3!), for 3 from 10

For a general x items from a population of n, it becomes

n!/((n-x)!*x!)