I don't understand how to do this problem. It's about permutations.

How many distinct arrangements are possible using the letters in the word CHEER?

Multiple Choice

-60

-50

-40

-20

The number of possible disinct arrangements =

[ Number of letters in the word ] ! / [ Repeats of any letter(s) ] !

So we have

[ 5 ] ! / [ number of repeated E's ] ! =

[ 5 ] ! / [ 2 ] ! =

120 / 2 =

60

a slightly different way of looking at it

\(\text{First choose two slots for the E's }\dbinom{5}{2}\\ \text{Then we have 3 distinct letters that we can make }3! \text{ arrangements with}\\ \dbinom{5}{2}3! = 10\cdot 6 = 60\)