If $^nC_r$ denotes the number of combinations of $n$ things taken $r$ at a time,then the expression $^nC_{r+1} + ^nC_{r-1} + 2 \times ^nC_r$ equals

$^{80}C_{40}$ is not divisible by -

How many words can be made from the letters of the word $DELHI$,if $L$ comes in the middle in every word?

$A$ man has $10$ friends. In how many ways can he invite one or more of them to a party?

There are $4$ notes of Rs. $100$ and $5$ other notes of denominations Rs. $1$,Rs. $2$,Rs. $5$,Rs. $20$,and Rs. $50$. These notes are to be distributed among $3$ children such that each child receives at least one note of Rs. $100$. Find the total number of ways of distribution.

If $33!$ is divisible by $2^n$,where $n \in N$,then the sum of all possible values of $n$ is: