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 × 7 × 6 × 5 × 4 × 3 × 2 × 1

= 40320.

2. 4! – 3! = 4 × 3 × 2 × 1 – 3 × 2 × 1

= 24 – 6

= 18.

Question 2.

Is 3! + 4! = 7!?

Solution:

3! = 3 × 2 × 1 = 6.

4! = 4 × 3 × 2 × 1 = 24.

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

= 6 + 24

= 30.

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

= 5040 ≠ L.H.S.

Hence, 3! + 4! ≠ 7!.

Question 3.

Compute \(\frac{8!}{6!×2!}\).

Solution:

Question 4.

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

Solution:

∴ 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

∴ 9 × 8 : 7 × 6 × 5

= 15120.