# Permutations and Combinations

This set of MCQs is designed to test the concept and learning of the chapter on Permutations and Combinations, we shall learn some basic counting techniques which will enable us to answer this question without actually listing 3-digit arrangements.

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If an event can occur in ‘m’ different ways, following which another event can occur in ‘n’ different ways, then the total numbers of occurrence of the events in the given order is __________________

m + n m – n m*n m/n

A child has 2 pencil and 3 erasers. In how many ways he can take a pencil and an eraser?

5 6 8 9

If there are 4 paths to travel from Delhi to Kanpur, then in how many ways a person can travel from Delhi to Kanpur and came back to Delhi?

4 8 12 16

Six boys and six girls sit along a line alternately in x ways and along a circle (again alternatively in y ways), then

x = y y = 12x x = 10y x = 12y

How many 3-letter words with or without meaning, can be formed out of the letters of the word, LOGARITHMS, if repetition of letters is not allowed

720 420 none of these 5040

If repetition of the digits is allowed, then the number of even natural numbers having three digits is

250 350 450 550

A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of at least 3 girls.

588

885

858

None of these

If ⁿC15 = ⁿC6 then, the value of ⁿC21 is

0

1

21

None of these

In how many ways can 12 people be divided into 3 groups where 4 persons must be there in each group?

None of these

12!/(4!)³

Insufficient data

12!/{3! × (4!)³}

The number of combination of n distinct objects taken r at a time be x is given by,

n/2Cr

n/2Cr/2

nCr/2

nCr

Four dice are rolled. The number of possible outcomes in which at least one dice show 2, is

1296

671

625

585

The number of ways in which 8 distinct toys can be distributed among 5 children, is

58

85

8P5

5P5

The value of P(n, n – 1), is

n

2n

n!

2n!

Quiz/Test Summary
Title: Permutations and Combinations
Questions: 13
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