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How many different 4-digit numbers have exactly two different digits?

 Dec 23, 2020
 #1
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How many different 4-digit numbers have exactly two different digits?

There are 576 four digit numbers that have exactly 2 different digits!

 Dec 24, 2020
 #2
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 I got my answer from here.

Guest Dec 24, 2020
 #3
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Neither digit is zero, 2 of each one

9C2*4!/(2!2!) = 9C2* 6 = 36*6 = 216

 

Zero plus one other number, 2 of each

9*3!/2! = 27

 

neither digit is zero, 3 of one and 1 of the other.

9C2*2*4 = 36*8 = 288

 

One digit is zero, 3 of one and 1 of the other.

9*3 = 27

 

216+27+288+27 = 558

 

 

Note: There is room here for error.

 Dec 29, 2020
edited by Melody  Dec 29, 2020

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