How do you find the number of distinct permutations possible with the letters of the word "degree" using all the letters?

1 Answer

Answer:

120

Explanation:

When we arrange all the letters, the number of permutations and the factorial of the count of the elements is the same - in this case it's #6!# And if the letters were all unique, such as ABCDEF, that'd be the final answer.

However, we have three e's, which means that we'll double and triple count arrangements. To eliminate them, we need to divide by the ways that the three e's can be internally arranged - and that answer is #3!#.

And so, putting it together, we get:

#(6!)/(3!)=(6xx5xx4xx3!)/(3!)=120#