Question

Show that 9! /3!6! + 9!/4!5! = 10!/4!6!

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

To show : $\frac{9!}{3!6!}+\frac{9!}{4!5!}=\frac{10!}{4!6!}$

Solution :

Taking RHS,

$RHS=\frac{9!}{3!6!}+\frac{9!}{4!5!}$

$RHS=\frac{9\times 8\times 7\times 6!}{3\times 2\times 1\times 6!}+\frac{9\times 8\times 7\times 6\times 5!}{4\times 3\times 2\times 1\times 5!}$

$RHS=3\times 4\times 7+9\times 2\times 7$

$RHS=84+126$

$RHS=210$

Taking LHS,

$LHS=\frac{10!}{4!6!}$

$LHS=\frac{10\times 9\times 8\times 7\times 6!}{4\times 3\times 2\times 1\times 6!}$

$LHS=10\times 3\times 7$

$LHS=210$

So, LHS=RHS

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Show that 9!/3!6! +9! /4!5! = 10! /4!6!​

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