Find out the answer to "How many permutations of the letters ABCDEFG contain..."

High School
Algebra
Pre-Algebra
Factors and multiples

generals336

Answered question

2021-10-10

How many permutations of the letters ABCDEFG contain the string CFGA?

Answer & Explanation

insonsipthinye

Skilled2021-10-11Added 83 answers

Definitions
Definition permutation (order is important):
$P (n, r) = \frac{n!}{(n - r)!}$
Definition combination (order is not important):
$C (n, r) = (\begin{matrix} n \\ r \end{matrix}) = \frac{n!}{r! (n - r)!}$
with $n! = n \cdot (n - 1) \cdot . . . \cdot 2 \cdot 1$ .
We treat the mentioned string as one single letter, thus we have then the possible letters CFG A,B,D,E. We then have 4 letters of which we want to select 4 letters.
n=4
r=4
Evaluate the definition of a permutation:
$P (4, 4) = \frac{4!}{(4 - 4)!} = \frac{4!}{0!} = 4 \neq 24$

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