Permutation and Combination – Class XI – Exercise 7.2

1: Evaluate

(i) 8!

(ii) 4! – 3!

Solution:

(i) 8! = 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 = 40320

(ii)4! = 1 × 2 × 3 × 4 = 24

3! = 1 × 2 × 3 = 6

4! – 3! = 24 – 6 = 18

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2: Is 3! + 4! = 7!?

Solution:

3! = 1 × 2 × 3 = 6

4! = 1 × 2 × 3 × 4 = 24

3! + 4! = 6 + 24 = 30

7! = 1 × 2 × 3 × 4 × 5 × 6 × 7 = 5040

3! + 4! ≠ 7!

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3. Compute ^8!/_(6!x2!)

Solution:

^8!/_(6!x2!) = ^8x7x6!/_6!x2x1 = ^8×7/₂ = 28

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4. If ¹/_6! + ¹/_7! = ¹/_8! , find x.

Solution:

¹/_6! + ¹/_7! = ¹/_8!

¹/_6! = ¹/_7×6! = ¹/_8x7x6!

¹/_6! (1+ ¹/_7!) = ¹/_8x7x6!

1 + ¹/₇ = ^x/_8×7

⁸/₇ = ^x/_8×7

x = ^8x8x7/₇

x = 64

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5. Evaluate ^n!/_(n-r)! , when

(i) n = 6, r = 2

(ii) n = 9, r = 5

Solution:

(i) n = 6, r = 2

^n!/_(n-r)! = ^6!/_(6-2)! = ^6!/_4! = ^6x5x4!/_4! = 30

(ii) n = 9, r = 5

^n!/_(n-r)! = ^9!/_(9-5)! = ^9!/_4! = ^9x8x7x6x5x4!/_4! = 15120

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