Re: How many positive integers less than 10,000 are there in which the sum
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26 Sep 2022, 07:20
There could be six cases:
Case I:
The four digits consist of 1, 1, 1, 2.
Total numbers that can be formed using these four digits: 4. (2 can be in any of the four places)
Case 2:
1, 1, 3, 0
Total numbers that can be formed: 12. (4!/2, using Mississippi Rule of combination)
Case 3:
1, 2, 2, 0
Total numbers that can be formed: 12. (4!/2, using Mississippi Rule of combination)
Case 4:
1, ,4, 0, 0
Total numbers that can be formed: 12. (4!/2, using Mississippi Rule of combination)
Case 5:
0, 0, 0, 5
Total numbers that can be formed:4. (5 can be in any four places)
Case 6:
2, 3, 0, 0
Total numbers that can be formed: 12. (4!/2, using Mississippi Rule of combination)
Grand total of numbes: 4+12+12+12+4+12 = 56. Choice C.
Cheers.