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(n-3)(n-4)!/(n-5)(n-6)!=?

Note by Mehdi Balti 2 years, 3 months ago

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Comment deleted Jul 20, 2015

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Can you explain it :)

@Mehdi Balti, could you please clarify what the problem is? Thanks.

It's factorial and the answer will be in positive integer.Not in decimal (n-3)(n-4)!/(n-5)(n-6)!=?

Based on how you've clarified the problem, I'm assuming you wish to find the value of

\[x = \frac{(n-4)!(n-3)}{(n-6)!(n-5)},\]

where \(x\) is a positive integer.

Note that

\[\begin{align} x &= \frac{(n-4)!(n-3)}{(n-6)!(n-5)} \nonumber \\ &= \frac{(n-3)[(n-4)(n-5)(n-6)\cdots(3)(2)(1)]}{(n-5)[(n-6)(n-7)(n-8)\cdots(3)(2)(1)]} \nonumber \\ &= \frac{(n-3)(n-4)(n-5)!}{(n-5)!} \nonumber \\ &= (n-3)(n-4) \nonumber \end{align}\]

This value is different for different values of \(n\). I'm not sure if this is what you want, although \((n-3)(n-4)\) is clearly a positive integer for positive integer values of \(n\). Please clarify further. Thanks!

Yes n value is positive integer.Really thanks @Victor Loh I got it completely Now :) Thumps up for u Cheers :)

If I would not given the value but say that it's positive integer then how would you solve this ?Answer should be in positive integer.

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TopNewestComment deleted Jul 20, 2015

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Can you explain it :)

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@Mehdi Balti, could you please clarify what the problem is? Thanks.

Log in to reply

It's factorial and the answer will be in positive integer.Not in decimal (n-3)(n-4)!/(n-5)(n-6)!=?

Log in to reply

Based on how you've clarified the problem, I'm assuming you wish to find the value of

\[x = \frac{(n-4)!(n-3)}{(n-6)!(n-5)},\]

where \(x\) is a positive integer.

Note that

\[\begin{align} x &= \frac{(n-4)!(n-3)}{(n-6)!(n-5)} \nonumber \\ &= \frac{(n-3)[(n-4)(n-5)(n-6)\cdots(3)(2)(1)]}{(n-5)[(n-6)(n-7)(n-8)\cdots(3)(2)(1)]} \nonumber \\ &= \frac{(n-3)(n-4)(n-5)!}{(n-5)!} \nonumber \\ &= (n-3)(n-4) \nonumber \end{align}\]

This value is different for different values of \(n\). I'm not sure if this is what you want, although \((n-3)(n-4)\) is clearly a positive integer for positive integer values of \(n\). Please clarify further. Thanks!

Log in to reply

Yes n value is positive integer.Really thanks @Victor Loh I got it completely Now :) Thumps up for u Cheers :)

Log in to reply

If I would not given the value but say that it's positive integer then how would you solve this ?Answer should be in positive integer.

Log in to reply