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### Question 1

In how many ways can 8 prizes be given to 4 students if each of them is equally eligible?

### Question 2

How many 4 digit numbers can be formed with a given set of 7 distinct digits?

### Question 3

2 men are standing in front of 3 cabins. In how many ways can they enter the cabins?

### Question 4

There are 7 trains between two stations A and B. In how many ways can a student go from A to B and return by any of the available trains?

### Question 5

The letters of the word 'JUPITER' have to be arranged such that the vowels come together. How many different ways are possible?

**A**

720.

**B**

730.

**C**

710.

**D**

740.

**Soln.**

**Ans: a**

This word has 7 letters, out of which 4 are consonants and 3 are vowels. The vowels have to occupy three contiguous positions. This triad can be arranged in 3! ways like this: we can place 3 vowels in first place, 2 in second place and 1 in the third place, giving 3 × 2 × 1 = 6 permutations. Next, we have to arrange the 4 consonants and the triad treated as one letter, giving 5! = 120 possibilities. So the total possibilities are 6 × 120 = 720.

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This Blog Post/Article "Permutations and Combinations Quiz Set 015" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2020-02-07. Published on: 2016-05-08