Number of different words that can be formed from all letters of word $APPLICATION$ such that two vowels never come together is -
$(45)7!$
$8!$
$6!7!$
$(32)6!$
Out of $6$ books, in how many ways can a set of one or more books be chosen
Total number of $6-$digit numbers in which only and all the five digits $1,3,5,7$ and $9$ appear, is
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
The value of $^{15}{C_3}{ + ^{15}}{C_{13}}$ is
What is the number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these
are face cards,