Question

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

Answer 1

(a)

`25* 24* 23* 22=(25!)/(21!)`

(b)

`25* 24* 23* 22=P(25,4)`

Explanation:

Quotient of factorials:

we are given

`25* 24* 23* 22`

we can multiply top and bottom term by 21!

`25* 24* 23* 22=(25* 24* 23* 22* 21!)/(21!)`

we can write as

`25* 24* 23* 22=(25!)/(21!)`

As a permutation:

we know permutation formula

`P(n,r)=(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* 24* 23* 22=P(25,4)`