If ${}^{10}P_r = 604800$ and ${}^{10}C_r = 120$,then $r =$

In how many ways can $5$ red and $4$ white balls be drawn from a bag containing $10$ red and $8$ white balls?

Out of $7$ consonants and $4$ vowels,the number of words consisting of $3$ consonants and $2$ vowels that can be formed is:

The number of ways of forming a committee of $6$ members out of $5$ Indians,$5$ Americans,and $5$ Australians such that there will be at least one member from each country in the committee is:

If the number of $5$-element subsets of the set $A = \{a_1, a_2, \dots, a_{20}\}$ of $20$ distinct elements is $k$ times the number of $5$-element subsets containing $a_4$,then $k$ is

Determine the number of $5$ card combinations out of a deck of $52$ cards if there is exactly one ace in each combination.