In how many ways can a football team of $11$ players be selected from $15$ players? In how many cases can a particular player be included?

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:

$A$ dictionary is printed consisting of $7$-letter words only that can be formed using the letters of the word $CRICKET$. If the words are arranged in alphabetical order,as in an ordinary dictionary,then the number of words before the word $CRICKET$ is:

$A$ teacher of a class wants to set $1$ question from each of $2$ exercises in a book. If there are $15$ and $12$ questions in the $2$ exercises respectively,then in how many ways can the $2$ questions be selected?

Find the number of ways in which two Americans,two British,one Chinese,one Dutch,and one Egyptian can sit at a round table so that persons of the same nationality are separated.

The number of ways in which $35$ apples can be distributed among $3$ boys so that each can have any number of apples,is