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avatar+935 

Answer: 3360

 Mar 16, 2019
 #1
avatar+935 
+1

I tried using cases such as 2 Ts, 1 T and 0 Ts, but apparently, I got the wrong answer.

 Mar 16, 2019
 #2
avatar
+1

[10 nPr 4] - [8 nPr 4] = 3,360

 Mar 16, 2019
 #3
avatar+935 
0

How did you get that?

dgfgrafgdfge111  Mar 16, 2019
 #4
avatar
+1

All these are equivalent:
1 - 10 nPr 4 - 8 nPr 4             =3,360 
2 - [10 nPr 4]/2 + [8 nPr 4]/2 =3,360
3 - 9 nPr 4 =3,024 + 3024/9   =3,360

Guest Mar 16, 2019
 #5
avatar+6196 
+2

\(\text{There are 2 T's}\\ \text{So let's look at permutations by how many T's they contain}\\ 0 - \dbinom{4}{0}\dbinom{8}{4}4! = 1680\\ 1 - \dbinom{4}{1}\dbinom{8}{3}3! = 1344 \\ 2 -\dbinom{4}{2}\dbinom{8}{2}2! = 336\\ \text{These sum to }n = 3360\)

Rom  Mar 17, 2019
edited by Rom  Mar 17, 2019
 #6
avatar+935 
0

Thanks to all of you!!!

dgfgrafgdfge111  Mar 18, 2019

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