+0

# Help

+1
108
2
+484

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

Feb 8, 2019

#1
+101086
+2

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

Feb 8, 2019
edited by CPhill  Feb 8, 2019
#2
+5172
+1

a slightly different way of looking at it

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

.
Feb 9, 2019