Question

Compute:
i) $\frac{10!}{3! \times 7!}$
ii) $\Big(\frac{9!-5!}{10!}\Big)$
iii) $\frac{8!}{6!-4!}$
iv) $\frac{8!}{(6-4)!}$

Answer 1

Answer:

i) 120

ii) 3023/30240

iii) 1680/29

Step-by-step explanation:

i) 10!/3!*7!

10! = 10 * 9 * 8 * 7!

10!/7! = 720

10!/3!*7! = 720/3!

= 720/3*2

= 720/6

= 120

ii) (9! - 5!)/10!

9! = 9 * 8 * 7 * 6 * 5!

9! - 5! = 9 * 8 * 7 * 6 * 5! - 5!

= 5!(9*8*7*6 - 1)

= 5!*3023

(9! - 5!)/10! = 3023*5!/10*9*8*7*6*5!

= 3023/30240

iii) 8!/6!-4!

6! = 6*5*4!

6! - 4! = 30*4! - 4!

= 29*4!

8! = 8*7*6*5*4! = 1680*4!

8!/6!-4! = 1680*4!/29*4!

= 1680/29

Hope, it helps !

Answer 2

Solution :

i) $\frac{10!}{3! \times 7!}$

= $\frac{10.9.8.7!}{(3.2.1)(7!)}$

= $\frac{10.9.8}{6}$

= $120$

ii) $\Big(\frac{9!-5!}{10!}\Big)$

= $\Big(\frac{9.8.7.6.5!-5!}{10!}\Big)$

= $\Big(\frac{(5!)(9.8.7.6-1)}{10.9.8.7.6.5!}\Big)$

= $\Big(\frac{3024-1}{10.9.8.7.6}\Big)$

= $\frac{3023}{30240}$

iii) $\frac{8!}{6!-4!}$

= $\frac{8.7.6.5.4!}{(6.5.4!-4!)}$

= $\frac{8.7.6.5.4!}{4!(30-1)}$

= $\frac{1680}{29}$

iv) $\frac{8!}{(6-4)!}$

= $\frac{8!}{(6-4)!}$

= $\frac{8.7.6.5.4.3.2.1}{2!}$

= $\frac{8.7.6.5.4.3.2.1}{2.1}$

= $8×7×6×5×4×3$

= $5040$

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