Combination with Constraints

Q. There are $7$ periods in each working day of a school. In how many ways can one organize $6$ subjects such that each subject is allowed atleast one period?

1. $120$
2. $126$
3. $1440$
4. $15120$

Q. A bag contains $4$ red, $3$ green and $5$ blue balls. In how many ways, $2$ red, $1$ green and $3$ blue balls can be drawn from the bag?

1. $19$
2. $18$
3. $180$
4. $60$

Q. The number of two-element subsets in the collection $4,5,6,7$ is

1. $8$
2. $6$
3. $12$
4. $7$

Q. In how many different ways can the letters of the word $CHASE$ be arranged such that the vowels always come together.

1. $48$
2. $24$
3. $12$
4. $72$

Q. Out of $8$ consonants and $3$ vowels, how many set of letters of $3$ consonants and $2$ vowels can be formed?

1. $168$
2. $120$
3. $20160$
4. $288$

Q. There is a group of $20$ people that has $12$ girls and $8$ boys. A team of $6$ players is to be formed from this group, having $3$ girls and $3$ boys. In how many ways can such a group be formed?

1. $11230$
2. $12130$
3. $1230$
4. $12320$