In how many ways can $5$ red and $4$ white balls be drawn from a bag containing $10$ red and $8$ white balls?

The number of ways in which $3$ children can distribute $10$ tickets out of $15$ consecutively numbered tickets among themselves such that they get consecutive blocks of $5, 3$ and $2$ tickets is:

$A$ customer forgets a $4$-digit code for an Automatic Teller Machine ($A$.$T$.$M$.) in a bank. However,he remembers that this code consists of digits $3, 5, 6$ and $9$. Find the largest possible number of trials necessary to obtain the correct code.

Choose the correct number of ways in which $15$ different books can be divided into five heaps of equal number of books.

$A$ father with $8$ children takes them $3$ at a time to the Zoological gardens,as often as he can without taking the same $3$ children together more than once. The number of times each child will go to the garden is

If $a$ denotes the number of permutations of $x + 2$ things taken all at a time,$b$ the number of permutations of $x$ things taken $11$ at a time,and $c$ the number of permutations of $x - 11$ things taken all at a time such that $a = 182bc$,then the value of $x$ is