How many different arrangements can be made with the letters in the word ROBERT if you use all of the letters?

Almost Geno :)

But there are 2 R's so I think that the answer is 

 

$$\frac{6!}{2!}=\frac{6!}{2}$$

 

$${\frac{{\mathtt{6}}{!}}{{\mathtt{2}}}} = {\mathtt{360}}$$   ways

k 6 characters in the name robert

6*6=36

overall, there should be 36 possible unique arrangements for the letters ROBERT

Since there are  6  different letters, you have  6  choices for the first letter.

Now, since there are  5  letters remaining, you have  5  choices for the second letter.

Then, you have  4  choices for the third letter;  3  choices for the fourth letter;  2  choices for the fifth leetter; and only  1  choice for the sixth, and last letter.

Multiplying these choices together:  6 x 5 x 4 x 3 x 2 x 1  =  6!  =  720 choices.