Question

How many permutations of the letters “a b c d e f g h” contain?

Answer 1

In this problem, we have to find how many permutations of the letters “a b c d e f g h” contain. Permutation determines the number of techniques that determines the number of possible arrangements in a set when the order of arrangement matters. We can also use formulas to find the answer. In this problem, we have a group of letters “a b c d e f g h”, which has 8 letters in it, we can either directly find the factorial for the given number of letters or we can use the permutation formula to find the answer.

Complete step by step solution:
We know that the given letters are “a b c d e f g h”.
Where there are 8 letters, n = 8, r = 8.
We know that the permutation formula is
Permutation, $^{n}{{P}_{r}}=\dfrac{n!}{\left( n-r \right)!}$
Where, n = 8, r = 8.
${{\Rightarrow }^{8}}{{P}_{8}}=\dfrac{8!}{\left( 8-8 \right)!}=\dfrac{8!}{1}=8\times 7\times 6\times 5\times 4\times 3\times 2\times 1=40320$

Therefore, there are 40320 permutation in the letters “a b c d e f g h”.

Note: We can also find the given permutation, as it has 8 letters in it, so we can just find the factorial for the given number of terms to find the factor.
We know that the given letters are “a b c d e f g h”.
We can see that there are 8 letters in it, so we can find the factorial of 8
$\Rightarrow 8!=8\times 7\times 6\times 5\times 4\times 3\times 2\times 1=40320$
Therefore, there are 40320 permutation in the letters “a b c d e f g h”