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Oxana [17]
3 years ago
6

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

Mathematics
1 answer:
Kipish [7]3 years ago
5 0

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)

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