Question

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

Answer 1

`" "`
A total of

`color(red)(7560` permutations are possible

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

Explanation:

`" "`
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 !")`

`rArr ["9 ! "]/("1 * 24 * 1 * 2 * 1 )`

`rArr (362,880)/48`

`rArr 7560`

Hence,

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

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

Hope it helps.