SOLUTION: A six digit number is to be formed using only digits from the set {1,2,3,5,6,7,9}. There are to be three distinct digits in the numbers formed, one of which appears four times and
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-> SOLUTION: A six digit number is to be formed using only digits from the set {1,2,3,5,6,7,9}. There are to be three distinct digits in the numbers formed, one of which appears four times and
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Question 1026955: A six digit number is to be formed using only digits from the set {1,2,3,5,6,7,9}. There are to be three distinct digits in the numbers formed, one of which appears four times and the other two, once each. How many different numbers are possible. Answer by richard1234(7193) (Show Source):
You can put this solution on YOUR website! Choose the digit that appears four times (7 ways), then choose the remaining two digits (say A and B). Assume that A and B are chosen with order important (6*5 = 30 ways) - you will see why later.
Choose four of the six placeholders for the digit that appears four times to occupy (6C4 = 15 ways). Then put A (the first of the 2 digits chosen) in the first unoccupied spot and B in the second unoccupied spot. This constructs such a number, and we know that we didn't overcount.
