SOLUTION: How many eight digit numbers are there in which appears 3 different digits where the largest digits appears twice and the other two appears three times each. Assume 0 cannot

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Question 1021790: How many eight digit numbers are there in which appears 3
different digits where the largest digits appears twice
and the other two appears three times each. Assume 0
cannot be used at all.
Found 2 solutions by Edwin McCravy, AnlytcPhil:
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
There are 9C3 ways to choose the 3 digits.

Each of those choices is made up of a largest digit, 
a middle-sized digit, and a smallest digit.

There are 8 places in an 8-digit number for the digits to go.

Choose the 2 places for the largest digit to go in 8C2 ways.
That leaves 6 places for the middle-sized digit.
Choose the 3 places for the middle-sized digit to go in 6C3 ways.
That leaves 3 places for the smallest digit.
Choose the places for the smallest digits to go in 3C3 of 1 way. 
(Only 1 way, because there are only 3 places left for the 
smallest digit).

Answer: (9C3)(8C2)(6C3)(3C3) = 47040 

Edwin
Answer by AnlytcPhil(1806)   (Show Source): You can put this solution on YOUR website!
This is to advise that although the answer 47040 to your
problem above is correct, I made a typo of "(5C3)" for 
"(6C3)" in the solution which I originally posted.  I have 
corrected it above as 

Answer: (9C3)(8C2)(6C3)(3C3) = 47040 

Edwin
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