# Â 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:Â  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 Ã— 5 Ã— 5 =125

(ii) If repetition of the digits is not allowed

Therefore, the total number of possible 3-digit numbers=5 Ã— 4 Ã— 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:Â  The 3 digit number is even if unit place number will be = 2, 4, 6

Therefore, the total number ofÂ  3-digit numbers = 6 Ã— 6 Ã— 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 codesÂ  =Â  10 Ã— 9 Ã— 8 Ã— 7Â  = 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: Â Given that the first 2 digits of each number are 67.

Therefore, the number is 67 Ã— Ã— Ã—

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

âˆ´ The total five-digit numbers with given conditions = 8 Ã— 7 Ã— 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.

âˆ´ The total number of possible outcomes after 3 times = 2 Ã— 2 Ã— 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 Ã— 4 = 20

### Chapter 6 Linear Inequalities Ncert math solution

Ex 6.1 Linear Inequalities ncert math solution class 11

Ex 6.2 Linear Inequalities ncert math solution class 11

Ex 6.3 Linear Inequalities ncert math solution class 11

Chapter 6 Miscellaneous ncert math solution class 11

### Chapter 7 Permutation and Combination Ncert math solution

Exercise 7.1 Permutation and Combination Ncert math solution

Exercise 7.2 Permutation and Combination Ncert math solution

Exercise 7.3 Permutation and Combination Ncert math solution

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