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### Question 1

Out of given 5 consonants and 4 vowels, how many words can be formed that contain 3 consonants and 2 vowels or 3 vowels and 2 consonants?

**A**

12000.

**B**

12010.

**C**

11990.

**D**

12020.

**Soln.**

**Ans: a**

We can make the selection in ^{4}C_{3} × ^{5}C_{2} + ^{4}C_{2} × ^{5}C_{3} ways. But the five members can themselves be arranged in 5! ways. So the number of words is 120 × (^{4}C_{3} × ^{5}C_{2} + ^{4}C_{2} × ^{5}C_{3}) = 12000.

### Question 2

5 men are standing in front of 7 cabins. In how many ways can they enter the cabins?

### Question 3

There are 8 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 4

How many words can be formed with 7 distinct consonants and 3 distinct vowels such that vowels stay together at the end of each word?

### Question 5

How many possible outcomes are there if a die with 6 faces is cast and then a coin with 2 sides is tossed?

This Blog Post/Article "Permutations and Combinations Quiz Set 003" 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