Question

Write 25*24*23*22 as a quotient of factorials and as a permutation

Answer 1

Answer:

(a)

$25\times 24\times 23\times 22=\frac{25!}{21!}$

(b)

$25\times 24\times 23\times 22=P(25,4)$

Step-by-step explanation:

Quotient of factorials:

we are given

$25\times 24\times 23\times 22$

we can multiply top and bottom term by 21!

$25\times 24\times 23\times 22=\frac{25\times 24\times 23\times 22\times 21!}{21!}$

we can write as

$25\times 24\times 23\times 22=\frac{25!}{21!}$

As a permutation:

we know permutation formula

$P(n,r)=\frac{n!}{(n-r)!}$

now, we can compare and find 'n' and 'r'

$n=25$

$n-r=21$

we can plug back n=25

$25-r=21$

$r=4$

so, we can write

$25\times 24\times 23\times 22=P(25,4)$