Permutation

In a group of $6$ boys and $5$ girls, $5$ students have to be selected. In how many ways it can be done so that at least $2$ boys are included

In how many ways $5$ Americans and $5$ Indians be seated along a circular table, so that they are seated in alternative positions

In how many ways $4$ Indians, $5$ Africans and $7$ Japanese be seated in row so that all person of same nationality sits together

There are $15$ points in a plane out of which $6$ are collinear. FInd the number of lines that can be formed from $15$ points.

There are bananas, $7$ apples and $6$ managoes in a fruit basket. In how many ways can a person make a selection of fruits from basket.

In how many different ways can the letter of the word ELEPHANT be arranged so that vowels always occur together?

How many $3$ digit number can be formed with the digits $5, 6, 2, 3, 7$ and $9$ which are divisible by $5$ and none of its digit is repeated?

In a group of $6$ boys and $8$ girls, $5$ students have to be selected. In how many ways it can be done so that at least $2$ boys are included

How many $3$ digit number can be formed by $0, 2, 5, 3, 7$ which is divisible by $5$ and none of the digit is repeated.

In how many different ways the letters of the world INSIDE be arranged in such a way that all vowels always come together

In party there is a total of $120$ handshakes. If all the persons shakes hand with every other person. Then find the number of person present in the party.

There are $15$ points in a plane out of which $6$ are collinear. Find the number of lines that can be formed from $15$ points.

In how many $8$ prizes can be given to $3$ boys, if all boys are equally eligible of getting the prize.

In how many ways $8$ Students can be given $3$ Prizes such that no student receives more than $1$ Prize?

How many $4$ digit words can be made from the digits $7, 8, 5, 0,$ and $4$ without repetition?

There are $6$ men and $7$ women. In how many ways a committee of $4$ members can be made such that a particular man is always to be excluded?

There are $8$ men and $7$ women. In how many ways a group of $5$ people can be made such that the particular woman is always to be included?

How many $3$ digits numbers have exactly one digit $2$ in the number?

In how many ways a group of $4$ men and $3$ women be made out of a total of $8$ men and $5$ women?

In how many ways all the letters of the word 'MINIMUM' be arranged that all vowels are together?