Total number of $3$ letter words that can be formed from the letters of the word $'SAHARANPUR'$ is equal to

The total number of four-digit numbers such that each of the first three digits is divisible by the last digit is equal to:

What is the total number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these are the four cards of the same suit?

$A$ letter lock consists of three rings with $15$ different letters each. If $N$ denotes the number of ways in which it is possible to make unsuccessful attempts to open the lock,then:

If $S_n = \sum_{r=0}^n \frac{1}{^nC_r}$ and $T_n = \sum_{r=0}^n \frac{r}{^nC_r}$,then $\frac{T_n}{S_n}$ is equal to

Let $a_1, a_2, \ldots, a_n$ be $n$ non-zero real numbers,of which $p$ are positive and the remaining are negative. The number of ordered pairs $(j, k)$ with $j < k$ for which $a_j a_k$ is positive is $55$. Similarly,the number of ordered pairs $(j, k)$ with $j < k$ for which $a_j a_k$ is negative is $50$. Then,the value of $p^2 + (n-p)^2$ is