If $^8{C_r}{ = ^8}{C_{r + 2}}$, then the value of $^r{C_2}$ is
$8$
$3$
$5$
$2$
$10$ different letters of English alphabet are given. Out of these letters, words of $5$ letters are formed. How many words are formed when at least one letter is repeated
The total number of ways of selecting six coins out of $20$ one rupee coins, $10$ fifty paise coins and $7$ twenty five paise coins is
If $^{2n}{C_3}:{\,^n}{C_2} = 44:3$, then for which of the following values of $r$, the value of $^n{C_r}$ will be 15
Determine $n$ if
$^{2 n} C_{3}:^{n} C_{3}=11: 1$
In an examination there are three multiple choice questions and each question has $4 $ choices. Number of ways in which a student can fail to get all answers correct, is