An urn contains $5$ red marbles,$4$ black marbles and $3$ white marbles. The number of ways in which $4$ marbles can be drawn so that at most three of them are red is

Out of $6$ boys and $4$ girls,a group of $7$ is to be formed. In how many ways can this be done if the group is to have a majority of boys?

The number of ordered pairs $(r, k)$ for which $6 \cdot ^{35}C_{r} = (k^{2} - 3) \cdot ^{36}C_{r+1}$,where $k$ is an integer,is

The least value of a natural number $n$ such that $\binom{n-1}{5} + \binom{n-1}{6} < \binom{n}{7}$ is:

$A$ 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

Find the number of ways of selecting $9$ balls from $6$ red balls,$5$ white balls,and $5$ blue balls if each selection consists of $3$ balls of each colour.