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How many 7-digit numbers can be formed using only the digits 1, 2, and 3, where the total of all digits equals 10?
- 77
- 14
- 15
- None of these
Correct answer: 77
Solution
With a ones, b twos and c threes, a+b+c=7 and a+2b+3c=10 give b+2c=3. So either (a,b,c)=(4,3,0) with 7!/(4!3!)=35 arrangements, or (5,1,1) with 7!/(5!1!1!)=42. Total = 35+42 = 77, so the answer is 77; stored 14 is wrong.
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