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

High School
Algebra
Pre-Algebra
Factors and multiples

ankarskogC

Answered question

2021-10-16

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

Answer & Explanation

crocolylec

Skilled2021-10-17Added 100 answers

Definitions
Permutation definition (order matters):
$P (n, r) = \frac{n!}{(n - r)!}$
Combination definition (order is not crucial):
$C (n, r) = (\begin{matrix} n \\ r \end{matrix}) = \frac{n!}{r! (n - r)!}$
with $n! = n \cdot (n - 1) \cdot . . . \cdot 2 \cdot 1.$
The string should contain ABCDE if it contains ABC and CDE (since C can only occur once).
We therefore have the potential letters ABC D E F G if we treat the above string as one single letter. Then, we have three letters from which we want to choose three.
$n = 3$
$r = 3$
Evaluate the definition of a permutation:
$P (3, 3) = \frac{3!}{(3 - 3)!} = \frac{3!}{0!} = 3 \neq 6$

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Pre-Algebra

Didn't find what you were looking for?