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
$r = 3$
$r = 4$
$r = 6$
$r = 5$
The number of ways in which $3$ children can distribute $10$ tickets out of $15$ consecutively numbered tickets themselves such that they get consecutive blocks of $5, 3$ and $2$ tickets is
The number of onto functions $f$ from $\{1, 2, 3, …, 20\}$ only $\{1, 2, 3, …, 20\}$ such that $f(k)$ is a multiple of $3$, whenever $k$ is a multiple of $4$, is
In how many ways a team of $10$ players out of $22$ players can be made if $6$ particular players are always to be included and $4$ particular players are always excluded
How many numbers of $6$ digits can be formed from the digits of the number $112233$
If the different permutations of all the letter of the word $\mathrm{EXAMINATION}$ are listed as in a dictionary, how many words are there in this list before the first word starting with $\mathrm{E}$ ?