Question

Find the number of permutations in the word calculus?

Answer 1

The number of permutations in a word can be found with factorials.

There are 8 letters in the word calculus. Of these 8 letters, there are two C's, two L's, and two U's.

We'll set up a fraction to find the number of permutations. The factorial of 8 will be used in the numerator. To account for the sets of repeating letters, we'll use the factorial of how many repeating letters there are and use them in the denominator:

2 C's, 2 L's, 2 U's

$\frac{8!}{2! \times 2! \times 2!} = \frac{40320}{2 \times 2 \times 2} = \frac{40320}{8} = 5040$

There are 5040 different permutations of the word calculus.