Find the number of ways to arrange the letters in the following words:

A: Ohio
B: Alabama
C: Illinois
D: Mississippi
E: Tennessee

I will assume we are not distinguishing between small and capital letters.

I will do one:
TENNESSEE
- 9 total, 2 N's , 4 E's, 2 S's

total number of ways
= 9!/(2!4!2!) = 3780

Can you see what I did ?

OHIO ----> 4!/(2!) = 12

try the others.

I don't understand how you got them? I have tried to figure this out and can't get the right answer on how you got your answers.

I got 144 for TENNESSEE (9*1*2*4*2) and I got 16 for OHIO (4*2*2). I don't understand how you got your numbers and if I am doing this wrong?

To find the number of ways to arrange the letters in a word, we need to use the concept of permutations.

1. A: Ohio
- The word 'Ohio' has 4 letters.
- In this case, all the letters are unique, so the number of ways to arrange them is given by the formula n!, where n is the number of letters.
- Therefore, the number of ways to arrange the letters in 'Ohio' is 4! = 4 x 3 x 2 x 1 = 24.

2. B: Alabama
- The word 'Alabama' has 7 letters, but there are repeating letters ('A', 'a', and 'a').
- To find the number of arrangements, we'll use the permutation formula with repeated letters.
- The formula is n! / (n1! x n2! x ...), where n is the total number of letters and n1, n2, ... represent the count of each repeating letter.
- In the case of 'Alabama', there are 6 different letters but with two repeating 'a's. So we have 7! / (2! x 1!) = 7 x 6 x 5 x 4 x 3 x 2 x 1 / (2 x 1) = 2520 / 2 = 1260.

3. C: Illinois
- The word 'Illinois' has 8 letters, but there are repeating letters ('l' and 'i').
- Using the same formula as above, we have 8! / (2! x 2!) = 40320 / (2 x 2) = 10080.

4. D: Mississippi
- The word 'Mississippi' has 11 letters, but there are repeating letters ('s', 's', 'i', 'i', 'p', 'p').
- Using the same formula as above, we have 11! / (2! x 2! x 1! x 4!) = 11! / (2 x 2 x 1 x 24) = 39916800 / 96 = 415800.

5. E: Tennessee
- The word 'Tennessee' has 9 letters, but there are repeating letters ('e', 'n', 'n').
- Using the same formula as above, we have 9! / (3! x 1! x 1!) = 362880 / (6 x 1 x 1) = 60480.

To summarize:
A: Ohio - 24 arrangements
B: Alabama - 1260 arrangements
C: Illinois - 10080 arrangements
D: Mississippi - 415800 arrangements
E: Tennessee - 60480 arrangements