In how many ways can a committee consisting of one or more members be formed out of $12$ members of the Municipal Corporation
$4095$
$5095$
$4905$
$4090$
The value of $r$ for which $^{20}{C_r}^{20}{C_0}{ + ^{20}}{C_{r - 1}}^{20}{C_1}{ + ^{20}}{C_{r - 2}}^{20}{C_2} + ...{ + ^{20}}{C_0}^{20}{C_r}$ is maximum is
At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are $10$ candidates and $4$ are of be selected, if a voter votes for at least one candidate, then the number of ways in which he can vote is
If $^{n} C_{8}=\,^{n} C_{2},$ find $^{n} C_{2}.$
How many words, with or without meaning, each of $3$ vowels and $2$ consonants can be formed from the letters of the word $INVOLUTE$?
In an election there are $8$ candidates, out of which $5$ are to be choosen. If a voter may vote for any number of candidates but not greater than the number to be choosen, then in how many ways can a voter vote