The sum of all $4$ digit numbers that can be formed by using the digits $2, 4, 6, 8$ (repetition of digits not allowed) is

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

In how many ways can a team of $10$ players be selected from $22$ players if $6$ particular players are always to be included and $4$ particular players are always excluded?

In an examination,Yamini has to select $4$ questions from each part. There are $6, 7,$ and $8$ questions in Part-$I,$ Part-$II,$ and Part-$III,$ respectively. What is the number of possible combinations in which she can choose the questions?

There are $m$ points on a straight line $AB$ and $n$ points on another line $AC$,none of them being the point $A$. Triangles are formed from these points as vertices when $(i)$ $A$ is excluded and $(ii)$ $A$ is included. Then the ratio of the number of triangles in the two cases is

If $^{10}C_r = ^{10}C_{r+2}$,then $^5C_r$ equals: