How many different words can be formed by jumbling the letters in the word $MISSISSIPPI$ in which no two $S$ are adjacent $?$

An urn contains $5$ red marbles, $4$ black marbles and $3$ white marbles. Then the number of ways in which $4$ marbles can be drawn so that at the most three of them are red is

In a shop there are five types of ice-creams available. A child buys six ice-creams.               

Statement $-1 :$ The number of different ways the child can buy the six ice-creams is $^{10}C_5.$ 

Statement $-2 :$ The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging $6 \,A's$ and $4 \,B's$ in a row.

There are $12$ volleyball players in all in a college, out of which a team of $9$ players is to be formed. If the captain always remains the same, then in how many ways can the team be formed

A committee of $7$ has to be formed from $9$ boys and $4$ girls. In how many ways can this be done when the committee consists of:

at least $3$ girls?

The number of groups that can be made from $5$ different green balls, $4$ different blue balls and $3$ different red balls, if at least $1$ green and $1$ blue ball is to be included