Question

How many arrangements of the letters in TATTOO are there, if the two O's are to be separated?

Answer 1

40

Answer 2

how did u get it lol?

Answer 3

it seems to be easier to count the number of ways you can rearrange the letters with the two O's together (at least to me anyways). So i would count the total number of ways you can rearrange the letters with no restrictions, then subtract the number of ways with the two O's together. That would leave all the ways with the two O's separate.

Answer 4

Total number of ways you can rearrange the letters with no restrictions is:
\[\frac{6!}{3!2!} = 60\]

Total number of ways to rearrange letters when the O's are next to each other:
\[\frac{5!}{3!} = 20\]

so 60-20 = 40

Answer 5

two o's together = 5!/3! ?

Answer 6

right.

Answer 7

oh k i don't get why its on 3!

Answer 8

i dont know how to explain it properly. The way i see it, I treat the 2 O's as one piece, so instead of 6 letters, there are 5. thats there the 5! comes from. 3 of those pieces are T's though, so i divide by 3!

Answer 9

i did the same way too but was not sure if it was correct

Answer 10

yeah, combinations always confuse me, its good to have someone to check your answers with lol :)

Answer 11

what do you mean by t's lol?

Answer 12

the T's in TATTOO

Answer 13

so you divide by the letters that appear more than once?

Answer 14

i treat the (OO) as one piece, so the question is now, how many ways can you rearrange the letters in TATT(OO).

There are 5 objects, the 3 T's, the A, and the (OO). Thats 5!
but, there are 3 T's, and if i have one arrangement, say ATT(OO)T, and i switch the T's around, you cant physically tell since they are the same. So to account for that, we divide by 3!.

Answer 15

oh i see lol thanks heaps for the explanation:)