How many permutations of the letters ABCDEFG contain the strings ABC and DE?

vestirme4

vestirme4

Answered question

2021-10-13

How many permutations of the letters ABCDEFG contain the strings ABC and DE?

Answer & Explanation

Mayme

Mayme

Skilled2021-10-14Added 103 answers

Definitions
Permutation definition (order matters):
P(n,r)=n!(nr)!
Combination definition (order is not crucial):
C(n,r)=(nr)=n!r!(nr)!
with n!=n(n1)...21.
We therefore have the potential letters ABC, D E, F, and G if we treat the above string as one single letter. Next, we want to choose 4 letters from the remaining 4 letters.
n=4
r=4
Evaluate the definition of a permutation:
P(4,4)=4!(44)!=4!0!=424

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