Correct Answers: | |

Wrong Answers: | |

Unattempted: |

### Question 1

The letters of the word 'VIOLET' have to be arranged such that the vowels occupy only the odd positions. How many different ways are possible?

**A**

36.

**B**

46.

**C**

26.

**D**

56.

**Soln.**

**Ans: a**

This word has 6 letters, out of which 3 are consonants and 3 are vowels. The vowels have to occupy three fixed odd positions. We can place 3 vowels in first odd place, 2 in second odd place and 1 in the third odd place, giving 3 × 2 × 1 = 6 permutations. This will be done with the consonants also. So the total possibilities are 6 × 6 = 36.

### Question 2

Out of given 6 consonants and 4 vowels, how many words can be formed that contain 3 consonants and 2 vowels or 3 vowels and 2 consonants?

**A**

21600.

**B**

21610.

**C**

21590.

**D**

21620.

**Soln.**

**Ans: a**

We can make the selection in ^{4}C_{3} × ^{6}C_{2} + ^{4}C_{2} × ^{6}C_{3} ways. But the five members can themselves be arranged in 5! ways. So the number of words is 120 × (^{4}C_{3} × ^{6}C_{2} + ^{4}C_{2} × ^{6}C_{3}) = 21600.

### Question 3

In how many ways can a secretary and general secretary be chosen from a committee of 13 members?

### Question 4

From a group of 6 boys and 7 girls, in how many ways can 2 boys and 2 girls be selected?

### Question 5

How many possible outcomes are there if a die with 5 faces is cast and then a coin with 2 sides is tossed?

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This Blog Post/Article "Permutations and Combinations Quiz Set 016" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2019-08-18.