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

Step-by-step explanation:

The word ''knickknack'' has repetition, so, rearrangements with repetitions are calculated with the formula

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:

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,

Solving all, we have:

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

the red lines denote the population of the bacteria after 35 hours. that would be 2,409.24. the y-intercept is the blue line which is 800 because that is the starting point. the equation used to make the graph is 800(1.032)^h, where h is the number of hours.

step-by-step explanation: