The number of ways in which we can select three numbers from $1$ to $30$ such that we exclude every selection consisting of all even numbers is

How many words can be formed using $3$ consonants and $2$ vowels from $5$ consonants and $4$ vowels?

The value of ${2^n} \{ 1 \cdot 3 \cdot 5 \cdots (2n - 3) \cdot (2n - 1) \}$ is

In a circus,there are $10$ cages for accommodating $10$ animals. Out of these,$4$ cages are so small that $5$ out of the $10$ animals cannot enter them. In how many ways is it possible to accommodate the $10$ animals in these $10$ cages?

Assuming the balls to be identical except for their color,the number of ways in which one or more balls can be selected from $10$ white,$9$ green,and $7$ black balls is:

All the arrangements,with or without meaning,of the word $FARMER$ are written excluding any word that has two $R$ appearing together. The arrangements are listed serially in the alphabetic order as in the English dictionary. Then the serial number of the word $FARMER$ in this list is .... .