Permutation & Combination Level-2 Quiz-3

1. A question paper consists of 20 ‘true or false’ questions. In how many ways can a candidate answer the entire paper?

2. There are 7 Science books, 6 Mathematics books and 5 English books. The number of ways in which one or
more books can be given away is?

3. In how many ways can 7 identical letters be placed into four envelopes A, B, C, D such that the two boxes A and B have at least one ball each?

4. If there are 3 routes from a city A to city B and 5 routes from city B to city C. Then what are the number of distinct routes from A to C through B?

5. In how many ways can the letters of the word INDORE be reordered so that no letter is in its original place?

6. In how many ways can one choose 4 letters from the word EFFERVESCENT such that either all four letters are of the same type or all 4 are different?

7. Find the number of ways 4 students and a teacher can be seated in 5 chairs such that the teacher always sits in the middle.

8. Find the number of positive integer solutions for the equation x + y + z = 20 where x ≥ 2, y ≥ 3, z ≥ 4.

9. 7 points are marked on a straight line and 6 points are marked on another line which is parallel to the first line. How many triangles can be formed with these points as vertices?

10. From numbers 8, 9, 10, 11, … 25; eight numbers are selected such that the greatest is 19. In how many ways can
these 8 numbers be permuted?