Answer:
(a)
[tex]25\times 24\times 23\times 22=\frac{25!}{21!}[/tex]
(b)
[tex]25\times 24\times 23\times 22=P(25,4)[/tex]
Step-by-step explanation:
Quotient of factorials:
we are given
[tex]25\times 24\times 23\times 22[/tex]
we can multiply top and bottom term by 21!
[tex]25\times 24\times 23\times 22=\frac{25\times 24\times 23\times 22\times 21!}{21!}[/tex]
we can write as
[tex]25\times 24\times 23\times 22=\frac{25!}{21!}[/tex]
As a permutation:
we know permutation formula
[tex]P(n,r)=\frac{n!}{(n-r)!}[/tex]
now, we can compare and find 'n' and 'r'
[tex]n=25[/tex]
[tex]n-r=21[/tex]
we can plug back n=25
[tex]25-r=21[/tex]
[tex]r=4[/tex]
so, we can write
[tex]25\times 24\times 23\times 22=P(25,4)[/tex]
