In how many ways can one girl and one boy be selected from a group of $15$ boys and $8$ girls?

From all the English alphabets,five letters are chosen and are arranged in alphabetical order. The total number of ways,in which the middle letter is $M$,is:

Consider a class of $5$ girls and $7$ boys. The number of different teams consisting of $2$ girls and $3$ boys that can be formed from this class,if there are two specific boys $A$ and $B$ who refuse to be members of the same team,is

If $^nC_r = 84$,$^nC_{r-1} = 36$,and $^nC_{r+1} = 126$,then $n$ equals

There are $15$ persons in a party and each person shakes hands with every other person exactly once. The total number of handshakes is:

The total number of all those $3$-digit numbers in which the sum of all the digits in each of them is $10$,is