How many 3 letter combinations can be created from the word "CHEESE"?  (no reusing letters, unless repeated in the word)  A20B9C28D34E60

Sure, I can help with that.

The word "CHEESE" has 6 letters, but only 4 are unique (C, H, E, S). The letter E is repeated 3 times.

When creating a 3-letter combination, we have 3 slots to fill.

For the first slot, we have 6 options (C, H, E, E, E, S).

For the second slot, if the first slot was filled with E, we still have 5 options left (C, H, E, E, S). If the first slot was filled with any other letter, we have 4 options left (H, E, E, E, S or C, E, E, E, S).

For the third slot, if the first two slots were filled with E, we still have 4 options left (C, H, E, S). If only one E was used, we have 3 options left (H, E, S or C, E, S). If no E was used, we have 2 options left (E, E).

So, we have to consider 3 scenarios:

1. No E is used: 4 options for the first slot, 3 for the second, and 2 for the third. This gives us 432 = 24 combinations.

2. One E is used: 5 options for the first slot, 4 for the second, and 3 for the third. This gives us 543 = 60 combinations.

3. Two E's are used: 6 options for the first slot, 5 for the second, and 4 for the third. This gives us 654 = 120 combinations.

However, in the third scenario, we are over-counting the combinations where two E's are used, because the two E's are indistinguishable. So, we need to divide by 2! (which is 2), giving us 120/2 = 60 combinations.

Adding up all the combinations from the three scenarios, we get 24 + 60 + 60 = 144 combinations.

So, none of the options A20, B9, C28, D34, E60 are correct. The correct answer should be 144.