Step-by-step explanation:
a).
n! is
[tex]n(n - 1)(n - 2)(n - 3)(n - 4).........(1)[/tex]
(n-3)! is
[tex](n - 3)(n - 4)(n - 5)..........(1)[/tex]
If we divide the two, everything behind (n-3) will just cancel out so we would be left with only
[tex](n)(n - 1)(n - 2)[/tex]
So the answer to a is
[tex]n(n - 1)(n - 2)[/tex]
b
Permutations formula of P(6,4) is
6!/(6-4)!, or 6!/2!.
[tex] \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{2 \times 1} = 360[/tex]
Then we divide by 4!
[tex] \frac{360}{4 \times 3 \times 2 \times 1} = 15[/tex]
The answer to b is 15
