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 $4$-digit numbers that can be formed from the digits $0, 1, 2, 3, 4, 5, 6, 7$ such that each number contains the digit $1$ is:

How many different four-letter words can be formed (the words need not be meaningful) using the letters of the word $MEDITERRANEAN$ such that the first letter is $E$ and the last letter is $R$?

Find $n$ if ${ }^{n} P_{4}=18 \cdot{ }^{n-1} P_{2}$.

If $^{15}C_{3r} = ^{15}C_{r+3}$,then the value of $r$ is

Out of $18$ points in a plane,no three are in the same straight line except five points which are collinear. The number of $(i)$ straight lines,$(ii)$ triangles which can be formed by joining them is