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

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 3² = 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 6² = 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 4⁴ = 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 × ⁴P₁ × ²P₁ = 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 4² = 16 different ways. (By the principle of counting.)