# How many different permutations can you make with the letters in the word seventeen?

Jul 27, 2018

$\text{ }$
A total of

color(red)(7560 permutations are possible

with the letters in the word color(blue)("Seventeen".

#### Explanation:

$\text{ }$
We can use the following formula:

If there are color(red)(n objects with color(blue)(r types, then

color(red)((n!)/("n_1 ! n_2 ! n_3 ! n_4 ! ...... n_r !)

The word given is : color(green)("Seventeen"

Observe that there is a total of color(red)(9 alphabets in the word.

The letter color(blue)("S" appears color(red)(1 time

The letter color(blue)("E" appears color(red)(4 times

The letter color(blue)("V" appears color(red)(1 time

The letter color(blue)("N" appears color(red)(2 times

The letter color(blue)("T" appears color(red)(1 time

We can calculate the different permutations as follows:

color(blue)(["9 ! "]/("1 ! 4 ! 1 ! 2 ! 1 !")

$\Rightarrow \left[\text{9 ! "]/(} 1 \cdot 24 \cdot 1 \cdot 2 \cdot 1\right)$

$\Rightarrow \frac{362 , 880}{48}$

$\Rightarrow 7560$

Hence,

A total of color(red)(7560 permutations are possible

with the letters in the word color(blue)("Seventeen".

Hope it helps.