Free Practice Question
PS · Problem Solving
705-805
Combinations
How many three-digit positive integers are there such that the tens digit is smaller than the hundreds digit but greater than the units digit?
Answer Choices
Correct answer marked belowA
60
B
72
C
96
120
Correct
E
144
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Explanation
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Official Explanation
Official
Solution: We have to select three distinct digits so that the Hundreds digit > Tens digit > Units digit. This can be solved by applying the combination method.
Case 1: We have to select any three distinct digits among these nine digits for hundreds digit except zero. (0,1,2,3,4,5,6,7,8,9). 9C3 = rac{9*8*7}{3!} = 84 ways.…
Case 1: We have to select any three distinct digits among these nine digits for hundreds digit except zero. (0,1,2,3,4,5,6,7,8,9). 9C3 = rac{9*8*7}{3!} = 84 ways.…
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What it tests
Whether you can count arrangements and selections correctly — permutations vs. combinations.
Common trap
Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.
Details
Difficulty
705-805
Type
PS
Category