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HELP PLEASE - Distributive property with !

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by Alyssa345 » Fri Jun 18, 2021 1:53 pm

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How does the GMAT book come up with

k(k-1)! = k!

I always come up with (kk!)-k as a result.
I really don't understand how they use distributive property in this one.
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Re: HELP PLEASE - Distributive property with !

by regor60 » Mon Jun 21, 2021 11:35 am
Multiplication can distribute over addition and subtraction.

You THINK that's what's going on here.

However, (k-1)! is not subtraction, it is multiplication, and equals
(k-1) x (k-2)x(k-3)...x 1.

So this is equivalent to k x [(k-1)(k-2)(k-3)...1], which equals

k(k-1)(k-2)(k-3)...1, which is the definition of k!
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Re: HELP PLEASE - Distributive property with !

by Brent@GMATPrepNow » Mon Jun 21, 2021 11:57 am
Alyssa345 wrote: ↑
Fri Jun 18, 2021 1:53 pm
 How does the GMAT book come up with

k(k-1)! = k!

I always come up with (kk!)-k as a result.
I really don't understand how they use distributive property in this one.
Here's an example:
6(6 - 1)! = 6(5!)
= (6)(5)(4)(3)(2)(1)
= 6!
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