Permutations and Combinations Quiz Set 003 | Maths Aptitude Quiz Questions and Mock Test on Permutations and Combinations Set 3 | mock tests for Bank PO, SSC Exams, SO Clerical Exam, GATE Exam, LIC AO, GIC AO, etc.

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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?

12000.

12010.

11990.

12020.

Soln.
Ans: a

We can make the selection in ⁴C₃ × ⁵C₂ + ⁴C₂ × ⁵C₃ ways. But the five members can themselves be arranged in 5! ways. So the number of words is 120 × (⁴C₃ × ⁵C₂ + ⁴C₂ × ⁵C₃) = 12000.

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Question 2

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

2520.

2525.

2518.

2521.

Soln.
Ans: a

The first has 7 options, the second has (7 - 1), and so on. This is expressed as ⁷P₅, which evaluates to 2520.

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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?

64.

69.

62.

65.

Soln.
Ans: a

The upward journey is possible in 8 ways, and the downward also in 8 ways. So the outcomes are 8 × 8 = 64.

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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?

30240.

30250.

30230.

30260.

Soln.
Ans: a

We have to basically create two parts - one containing 7 consonants and the other containing 3 vowels. The consonants can be arranged in 7 ! ways, and vowels in 3 ! ways. The total count will be 7 ! × 3 ! = 30240.

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