Gujarat Board GSEB Textbook Solutions Class 11 Maths Chapter 7 Permutations and Combinations Ex 7.2 Textbook Questions and Answers.

## Gujarat Board Textbook Solutions Class 11 Maths Chapter 7 Permutations and Combinations Ex 7.2

Question 1.

Evaluate:

- 8!
- 4! – 3!

Solution:

1. 8! = 8 Ã— 7 Ã— 6 Ã— 5 Ã— 4 Ã— 3 Ã— 2 Ã— 1

= 40320.

2. 4! – 3! = 4 Ã— 3 Ã— 2 Ã— 1 – 3 Ã— 2 Ã— 1

= 24 – 6

= 18.

Question 2.

Is 3! + 4! = 7!?

Solution:

3! = 3 Ã— 2 Ã— 1 = 6.

4! = 4 Ã— 3 Ã— 2 Ã— 1 = 24.

So, L.H.S. = 3! + 4!

= 6 + 24

= 30.

Now, R.H.S. = 7! = 7 Ã— 6 Ã— 5 Ã— 4 Ã— 3 Ã— 2 Ã— 1

= 5040 â‰ L.H.S.

Hence, 3! + 4! â‰ 7!.

Question 3.

Compute \(\frac{8!}{6!Ã—2!}\).

Solution:

Question 4.

If \(\frac{1}{6!}\) + \(\frac{1}{7!}\) = \(\frac{x}{8!}\), find x?

Solution:

âˆ´ x = 64.

Question 5.

Evaluate \(\frac{n!}{n – r}\), when

(i) n = 6, r = 2

(ii) n = 9, r = 5

Solution:

(i) n = 6, r = 2

âˆ´ 9 Ã— 8 : 7 Ã— 6 Ã— 5

= 15120.