Odisha State Board Elements of Mathematics Class 11 Solutions CHSE Odisha Chapter 8 Permutations and Combinations Ex 8(a) Textbook Exercise Questions and Answers.

## CHSE Odisha Class 11 Math Solutions Chapter 8 Permutations and Combinations Exercise 8(a)

Question 1.

What is the total number of functions that can be defined from the set {1, 2} to the set {1, 2, 3}?

Solution:

The total number of functions that can be defined from the set {1, 2} to the set {1, 2, 3} is 3^{2} = 9.

Question 2.

A die of six faces marked with the integers 1, 2, 3, 4, 5, and 6 one on each face is thrown twice in succession, what is the total number of outcomes thus obtained?

Solution:

A die of six faces marked with the integers 1, 2, 3, 4, 5, and 6 one on each face, is thrown twice in succession.

∴ The total number of outcomes is 6^{2} = 36.

Question 3.

Five cities A, B, C, D, and E are connected to each other by straight roads. What is the total number of such roads?

Solution:

Five cities A, B, C, D, and E are connected to each other by straight roads.

∴ The number of such roads is \(\frac{{ }^5 \mathrm{P}_2}{2 !}\) = 10

Question 4.

What is the total number of different diagonals of a given pentagon?

Solution:

The total number of different diagonals of a given pentagon is

\(\frac{{ }^5 \mathrm{P}_2}{2 !}\) – 5 = 10 – 5 = 5

Question 5.

There are two routes joining city A to city B and three routes joining B to city C. In how many ways can a person perform a journey from A to C?

Solution:

There are two routes joining city A to city B and three routes joining B to city C.

∴ By the fundamental principle of counting, the total number of journeys in which a person can perform from A to C is 2 × 3 = 6.

Question 6.

How many different four-lettered words can be formed by using the four letters a, b, c, and d, while the letters can be repeated?

Solution:

The number of different words that can be formed by using the four letters a, b, c, and d, while the letters can be repeated is 4^{4} = 256.

Question 7.

What is the sum of all three-digit numbers formed by using the digits 1, 2, and 3?

Solution:

The 3-digit numbers that can be formed by using the digits 1, 2, and 3 are 123, 132, 213, 231, 312, and 321.

∴ Their sum = 1332.

Question 8.

How many different words with two letters can be formed by using the letters of the word JUNGLE, each containing one vowel and one consonant?

Solution:

The word ‘Jungle’ contains 2 vowels and 4 consonants. Each word contains one vowel and one consonant.

The number of different words formed.

2 × ^{4}P_{1} × ^{2}P_{1} = 2 × 4 × 2 = 16

Question 9.

There are four doors leading to the inside of a cinema hall. In how many ways can a person enter into it and come out?

Solution:

There are four doors leading to the inside of a cinema hall. A person can enter into it and come out in 4^{2} = 16 different ways. (By the principle of counting.)