Answer:
Step-by-step explanation:
The word ''knickknack'' has repetition, so, rearrangements with repetitions are calculated with the formula [tex]P=\frac{n!}{r! s! t!}[/tex]
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: [tex]P=\frac{10!}{4!2!2!}[/tex]
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, [tex]P=\frac{10.9.8.7.6.5.4.3.2.1}{(4.3.2.1)(2.1.)(2.1.)}[/tex]
Solving all, we have: [tex]P=37800[/tex]
Therefore, there are 37800 ways to rearrange the letter of the word ''knickknack''
