Total number of $6-$digit numbers in which only and all the five digits $1,3,5,7$ and $9$ appear, is
$\frac{5}{2}(6 !)$
$5^6$
$\frac{1}{2}(6 !)$
$6!$
Number of different words that can be formed from all letters of word $APPLICATION$ such that two vowels never come together is -
If $^{15}{C_{3r}}{ = ^{15}}{C_{r + 3}}$, then the value of $r$ is
If $^{2017}C_0 + ^{2017}C_1 + ^{2017}C_2+......+ ^{2017}C_{1008} = \lambda ^2 (\lambda > 0),$ then remainder when $\lambda $ is divided by $33$ is-
In how many ways can $5$ red and $4$ white balls be drawn from a bag containing $10$ red and $8$ white balls
Determine $n$ if
$^{2 n} C_{3}:\,^{n} C_{3}=12: 1$