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+0  
 
+1
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avatar+479 

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
avatar+99582 
+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

 

cool cool cool

 Feb 8, 2019
edited by CPhill  Feb 8, 2019
 #2
avatar+4810 
+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

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