Permutation & Combination Level-3 Quiz-3

1. There are 4 letters and 4 directed envelopes. What are the number of ways in which all the letters can be put into wrong envelope?

2. How many 10 digit numbers can be written using digits 5 and 6?

3. Find the number of non-negative integral solutions of 2x+2y+z=10?

4. In how many ways, 4 men and 4 women can be seated in a row such that men and women are alternate?

5. In how many ways, the faces of a cube can be painted with 6 different colors?

6. A person invites his 10 friends to a party and places 5 of them at one round table and other five at another round table. Find the number of ways in which he can arrange his friends.

7. In the above question, find the no. of ways in which he can arrange 4 friends at one round table and rest 6 at other.

8. A new flag is to be designed with six vertical stripes using some or all of the colors yellow, green, blue and red. Then, the number
of ways this can be done such that no two adjacent stripes have the same color out is?

9. There are 6 tasks and 6 persons. Task I cannot be assigned either to person 1 or to person 2; task 2 must be assigned to either
person 3 or person 4. Every person is to be assigned one task. In how many ways can the assignment be done?

10. Suppose you have a currency, named Miso, in three denominations: 1 Miso, 10 Misos and 50 Misos. In how many ways can you
pay a bill of 107 Misos?