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
$^{22}{C_{10}}$
$^{18}{C_3}$
$^{12}{C_4}$
$^{18}{C_4}$
In how many ways can a committee be formed of $5$ members from $6$ men and $4$ women if the committee has at least one woman
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 $\mathrm{E}$ ?
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
If ${a_n} = \sum\limits_{r = 0}^n {} \frac{1}{{^n{C_r}}}$ then $\sum\limits_{r = 0}^n {} \frac{r}{{^n{C_r}}}$ equals
The number of $4$ letter words (with or without meaning) that can be formed from the eleven letters of the word $'EXAMINATION'$ is