In how many ways can a team of $10$ players be selected from $22$ players if $6$ particular players are always to be included and $4$ particular players are always excluded?

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

How many words of $4$ consonants and $3$ vowels can be formed from $6$ consonants and $5$ vowels?

The least value of the natural number $n$ satisfying $C(n, 5)+C(n, 6)>C(n+1, 5)$ is

Consider three boxes,each containing $10$ balls labelled $1, 2, \dots, 10$. Suppose one ball is randomly drawn from each of the boxes. Denote by $n_i$ the label of the ball drawn from the $i^{th}$ box,$(i = 1, 2, 3)$. Then,the number of ways in which the balls can be chosen such that $n_1 < n_2 < n_3$ is:

If $\binom{n+1}{3} = 2 \times \binom{n}{2}$,then $n = \dots$