How many $2$ digit even numbers can be formed from the digits $1, 2, 3, 4, 5$ if the digits can be repeated?

Ten chairs are numbered as $1$ to $10$. Three women and two men wish to occupy one chair each. First,the women choose the chairs marked $1$ to $6$,then the men choose the chairs from the remaining. The number of possible ways is

In a library,there are $a$ books of type $A$,$2$ books of type $B$,$3$ books of type $C$,and $1$ book of type $D$. In how many ways can these books be arranged?

Let $P$ be the set of seven-digit numbers with the sum of their digits equal to $11$. If the numbers in $P$ are formed by using the digits $1, 2,$ and $3$ only,then the number of elements in the set $P$ is:

$a, b, c$ are three particular speakers among the $10$ speakers of a meeting. The number of ways of arranging all the $10$ speakers on the dais in a row so that all the three speakers $a, b, c$ do not sit together is

In how many of the distinct permutations of the letters in $MISSISSIPPI$ do the four $I$'s not come together?