Question 642890
If repetition is NOT allowed (ex: RTX is allowed, but RTT is NOT allowed)


Case 1) First letter is R


There are 6 letters total. After picking R, you have 5 left. So there are 5*4 = 20 ways to arrange the remaining letters in the remaining two slots.


Case 2) Second letter is R


Same as case 1, but now the R is in the second slot instead of the first. There are still 5 letters left and 5*4 = 20 ways to arrange these 5 remaining letters in the two outer slots.


Case 3) Third letter is R


Same as case 1, but now R is in slot 3. So there are 20 ways to arrange the remaining letters.



So we have 3 cases with 20 ways each giving us 3*20 = <font color="red">60</font> ways total.


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OR

If repetition is allowed (ex: RTT is finally allowed), then...


You have 6 letters, but you can only have exactly one R. So once you choose that R (for say the first slot), then you have 5 letters left to choose from for the second slot. Since repetition is allowed, you also have 5 letters left to choose for the 3rd slot.


So you have 5*5 = 25 ways to choose an R for the first slot, then 2 (maybe repeating) letters for the second and third slot.


This can be generalized if R was in any slot. So there are 3 times as many ways, which means that there are 3*25 = <font color="red">75</font> different ways


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Summary:


So again, if repetition is NOT allowed, then there are <font color="red">60</font> ways to do this.


If repetition is allowed, then there are <font color="red">75</font> ways to do this.