How many distinct ways can the letters of the word tooth be arranged?

30

5!/(2!2!) - 5 being the number of letters in the word and the 2s being the letters that are being repeated (T and O)

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

answer: he is 272195

step-by-step explanation: all you have to do is multiple 3535 and 77 and it equals 272195