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
Algebra ->
Permutations
-> 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
Log On
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):
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
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
