In how many ways can a set of five letters

Clifton Sanchez

Clifton Sanchez

Answered question

2021-11-12

In how many ways can a set of five letters be selected from the English alphabet?

Answer & Explanation

Upout1940

Upout1940

Beginner2021-11-13Added 9 answers

Definitions
Definition permutation (order is important):
P(n,r)=n!(nr)!
Definition combination (order is not important):
C(n,r)=(nr)=n!r!(nr)!
with nn(n1)21
Solution:
The order of the letters is not important, thus we need to use the definition of combination.
There are 26 letters in the English alphabet, of which we want to select 5.
n=26
r=5
Ebaluate the definition of a combination:
C(26,5)=26!5!(265)!=26!5!21!=65780

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