# In how many ways can you rearrange the letters A, B, C, D, E?

Jul 20, 2018

color(chocolate)(5! = 1 * 2 * 3 * 4 * 5 = 120 " ways"

#### Explanation:

"Formula for permutation " nPr = (n! )/ ((n-r)!)

$\text{Given " n = 5, (A, B, C, D, E) " " & " } r = 5 , \left(A , B , C , D , E\right)$

:. nPr = nPn = (n!) / ((n - n)! )= (n!) / 1 = 5!

color(chocolate)(5! = 1 * 2 * 3 * 4 * 5 = 120 " ways"

$120$

#### Explanation:

The total number of linear arrangements obtained from $n = 5$ different letters $A , B , C , D , E$ is given as

${\setminus}^{n} {P}_{n}$

$= {\setminus}^{5} {P}_{5}$

=5!

$= 5 \setminus \times 4 \setminus \times 3 \setminus \times 2 \setminus \times 1$

$= 120$