$^{20}C_1 + 3 ^{20}C_2 + 3 ^{20}C_3 + ^{20}C_4$ is equal to-
$^{20}C_4$
$2. ^{21}C_4$
$2. ^{22}C_4$
$^{23}C_4$
If $n$ is even and the value of $^n{C_r}$ is maximum, then $r = $
The number of ways in which $21$ identical apples can be distributed among three children such that each child gets at least $2$ apples, is
In how many ways can the letters of the word $\mathrm{ASSASSINATION} $ be arranged so that all the $\mathrm{S}$ 's are together?
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 $\mathrm{E}$ ?
In how many ways can a girl and a boy be selected from a group of $15$ boys and $8 $ girls