Question

How many distinct rearrangements of the letters in "knickknack" are there? Give your answer as an integer.

Answer 1

37,800

Explanation:

The word ''knickknack'' has repetition, so, rearrangements with repetitions are calculated with the formula
`P=(n!)/(r! s! t!)`

n is the total number of letter.

Letters above r, s and t, refers to the number of repetitions, in this case 3 letter repeat: k, n and c.

So, applying all this we have:
`P=(10!)/(4!2!2!)`

So, there are 10 letter, k repeats 4 times, n and c repeat twice

The sign ''!'' means that is a factorial operation, which is solved multiplying in a regressive way, for example: 4! = 4x3x2x1.

Then,
`P=(10.9.8.7.6.5.4.3.2.1)/((4.3.2.1)(2.1.)(2.1.))`

Solving all, we have:
`P=37800`

Therefore, there are 37800 ways to rearrange the letter of the word ''knickknack''