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.
HELP PLEASE - Distributive property with !
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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!
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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Here's an example:
6(6 - 1)! = 6(5!)
= (6)(5)(4)(3)(2)(1)
= 6!