$A$ code word is to consist of $2$ English alphabets followed by $2$ distinct numbers between $1$ and $9$. For example,$CA23$ is a code word. How many such code words are there?

$1 + \sum\limits_{r = 0}^{22} {\left\{ {r\left( {r + 2} \right) + 1} \right\}} \cdot r! = k!$,then the number of divisors of $k$ is

$A$ car can hold $2$ people in the front seat and $1$ person in the rear seat. If among $6$ persons $2$ can drive,then the number of ways in which the car can be filled is

How many different nine-digit numbers can be formed from the digits of the number $223355888$ by rearranging the digits so that the odd digits occupy even places?

$A$ man $X$ has $7$ friends,$4$ of them are ladies and $3$ are men. His wife $Y$ also has $7$ friends,$3$ of them are ladies and $4$ are men. Assume $X$ and $Y$ have no common friends. The total number of ways in which $X$ and $Y$ together can throw a party inviting $3$ ladies and $3$ men,such that $3$ friends of each of $X$ and $Y$ are in this party,is:

The number of arrangements of the letters of the word $SATAYPAUL$ such that no two $A$ are together and the middle letter is a consonant,is