Solved: "How many permutations of the letters ABCDEFG contain..."

High School
Algebra
Pre-Algebra
Factors and multiples

BenoguigoliB

Answered question

2021-10-14

How many permutations of the letters ABCDEFG contain the strings BA and GF?

Answer & Explanation

hesgidiauE

Skilled2021-10-15Added 106 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 B A, GF, C,D,E.
We then have 5 letters of which we want to select 5 letters.
$n = 5$
$r = 5$
Evaluate the definition of a permutation:
$P (5, 5) = \frac{5!}{(5 - 5)!} = \frac{5!}{0!} = 5 \neq 120$

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