Check the solution to "How many permutations of the letters ABCDEFG contain..."

High School
Algebra
Pre-Algebra
Factors and multiples

Aneeka Hunt

Answered question

2021-10-17

How many permutations of the letters ABCDEFG contain the strings CBA and BED?

Answer & Explanation

falhiblesw

Skilled2021-10-18Added 97 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 $n! = n \cdot (n - 1) \cdot . . . \cdot 2 \cdot 1$ .
A string cannot contain both CBA and Bed, since the string can only contain B once and B cannot be followed directly by an A and an E (there is only one element directly after B). Thus there are 0 strings that contain both CBA and BED.

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