**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

**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!

**Compute**^{8!}/_{(6!x2!)}

Solution:

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

**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

**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