The number of four-digit numbers formed by using the digits $0, 2, 4, 5$ (without repetition) which are not divisible by $5$ is:

In an examination,there are $5$ multiple choice questions with $3$ choices each,out of which exactly one is correct. There are $3$ marks for each correct answer,$-2$ marks for each wrong answer,and $0$ marks if the question is not attempted. The number of ways a student appearing in the examination can get exactly $5$ marks is:

$2^n \{1 \cdot 3 \cdot 5 \cdot \dots \cdot (2n - 3) \cdot (2n - 1)\} = \dots$

The number of integers lying between $1000$ and $10000$ such that every number contains the digits $3$ and $7$ exactly once without repetition is:

Assuming that the balls of the same color are identical,find the number of ways to select one or more balls from $10$ white,$9$ green,and $7$ black balls.

$A$ man has $7$ relatives,$4$ of them are ladies and $3$ are gents; his wife has $7$ other relatives,$3$ of them are ladies and $4$ are gents. The number of ways they can invite $3$ ladies and $3$ gents to a party such that there are $3$ of the man's relatives and $3$ of the wife's relatives,is: