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

If $2 \times {}^nC_5 = 9 \times {}^{n-2}C_5$,then the value of $n$ is:

$A$ student is asked to answer $10$ out of $13$ questions in an examination such that he must answer at least four questions from the first five questions. The number of choices available to him is

$A$ bag contains $3$ coins of one rupee,$4$ coins of fifty paise,and $5$ coins of ten paise. If at least one coin is selected from the bag,what is the total number of ways to make the selection?

Out of $6$ books,in how many ways can a set of one or more books be chosen?

In how many ways can we select any $4$ letters from the word $CORGOO$?