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Exercise 4.1 · Q14

Q.Find the value of

(i) 6!6!
(ii) 4!+5!4!+5!
(iii) 3!−2!3!-2!
(iv) 3!×4!3!\times 4!
(v) 12!9!×3!\dfrac{12!}{9!\times 3!}
(vi) (n+3)!(n+1)!\dfrac{(n+3)!}{(n+1)!}
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Use n!=n(n−1)!n!=n(n-1)! to cancel common factorial factors quickly.

Step 1. (i) 6!=7206!=720.

Step 2. (ii) 4!+5!=24+120=1444!+5!=24+120=144.

Step 3. (iii) 3!−2!=6−2=43!-2!=6-2=4.

Step 4. (iv) 3!×4!=6×24=1443!\times4!=6\times24=144.

Step 5. (v) 12!9!×3!=12×11×10×9!9!×3!=12×11×106=220\dfrac{12!}{9!\times3!}=\dfrac{12\times11\times10\times9!}{9!\times3!}=\dfrac{12\times11\times10}{6}=220. …

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