Exercise 7.1(Permutations and Combinations)

Ncert math solution(Exercise 7.1 ncert solutions maths class-11)

Question 1: How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5, assuming that

(i) Repetition of the digits is allowed?

(ii) Repetition of the digits is not allowed?

Solution: 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5

(i) If repetition of the digits is allowed

Then, the total number 3-digit numbers = 5 × 5 × 5 =125

(ii) If repetition of the digits is not allowed

Therefore, the total number of possible 3-digit numbers=5 × 4 × 3=60

Question 2: How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?

Solution: The 3 digit number is even if unit place number will be = 2, 4, 6

Therefore, the total number of 3-digit numbers = 6 × 6 × 3 = 108

Question 3: How many 4-letter codes can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?

Solution:- letter codes can be formed using the first 10 letters of the English alphabet, if no letter can be repeated

Therefore, the total number of 4-digit codes = 10 × 9 × 8 × 7 = 5040

Question 4: How many 5-digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once?

Solution: Given that the first 2 digits of each number are 67.

Therefore, the number is 67 × × ×

As repetition is not allowed and 6 and 7 are already taken, the digits available 0, 1, 2, 3, 4, 5, 8, 9. The number of possible digits is 8. .

∴ The total five-digit numbers with given conditions = 8 × 7 × 6 = 336

Question 5: A coin is tossed 3 times, and the outcomes are recorded. How many possible outcomes are there?

Solution: Given, A coin is tossed 3 times, and the outcomes are recorded.

The possible outcomes after a coin toss are head and tail.

The number of possible outcomes at each coin toss is 2.

∴ The total number of possible outcomes after 3 times = 2 × 2 × 2 = 8

Question 6: Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags, one below the other?

Solution: Given, 5 flags of different colours.

We know the signal requires 2 flags.

The number of ways in which signal can be given = 5 × 4 = 20