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

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Answer 1 · 2018-07-27T19:52:31

$" "$
A total of

$7560$ $color(red)(7560$ permutations are possible

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

$" "$
We can use the following formula:

If there are $n$ $color(red)(n$ objects with $r$ $color(blue)(r$ 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.