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

Suppose Anil's mother wants to give $5$ whole fruits to Anil from a basket of $7$ red apples,$5$ white apples,and $8$ oranges. If in the selected $5$ fruits,at least $2$ oranges,at least $1$ red apple,and at least $1$ white apple must be included,then the number of ways Anil's mother can offer $5$ fruits to Anil is $........$

$A$ group consists of $8$ boys and $5$ girls. The number of committees of $5$ persons that can be formed,if the committee consists of at least $2$ girls and at most $2$ boys,is:

The English alphabet has $5$ vowels and $21$ consonants. How many words with two different vowels and two different consonants can be formed from the alphabet?

The number of ways in which one or more balls can be selected out of $10$ white,$9$ green,and $7$ blue balls is:

How many words of $4$ consonants and $3$ vowels can be formed from $6$ consonants and $5$ vowels?