The number of ways five alphabets can be chosen from the alphabets of the word $MATHEMATICS$, where the chosen alphabets are not necessarily distinct, is equal to :
$175$
$181$
$177$
$179$
In how many ways a team of $11$ players can be formed out of $25$ players, if $6$ out of them are always to be included and $5$ are always to be excluded
A committee of $7$ has to be formed from $9$ boys and $4$ girls. In how many ways can this be done when the committee consists of:
exactly $3$ girls $?$
The total number of different combinations of one or more letters which can be made from the letters of the word ‘$MISSISSIPPI$’ is
In how many ways can $5$ girls and $3$ boys be seated in a row so that no two boys are together?
The number of values of $'r'$ satisfying $^{69}C_{3r-1} - ^{69}C_{r^2}=^{69}C_{r^2-1} - ^{69}C_{3r}$ is :-