Lorena Beard

2022-07-06

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

Leslie Rollins

Expert

Step 1
A total of 7560 permutations are possible with the letters in the word Seventeen.
Explanation:
We can use the following formula:
If there are n objects with r types, then $\frac{n!}{\text{}{n}_{1}!{n}_{2}!{n}_{3}!{n}_{4}!......{n}_{r}!}$.
The word given is :
Seventeen
Observe that there is a total of 9 alphabets in the word.
The letter S appears 1 time
The letter E appears 4 times
The letter V appears 1 time
The letter N appears 2 times
The letter T appears 1 time
Step 2
We can calculate the different permutations as follows:
$\frac{\text{9 !}\phantom{\rule{1ex}{0ex}}}{\text{1 ! 4 ! 1 ! 2 ! 1 !}}$
$⇒\frac{\text{9 !}\phantom{\rule{1ex}{0ex}}}{\text{}1\cdot 24\cdot 1\cdot 2\cdot 1}$
$⇒\frac{362,880}{48}$
$⇒7560$
Hence, a total of 7560 permutations are possible with the letters in the word Seventeen.

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