Free Practice Question
PS · Problem Solving
705-805
Combinations
Of the three-digit integers greater than 700, how many have two digits that are equal to each other and the remaining digit different from the other two?
Answer Choices
Correct answer marked belowA
90
B
82
80
Correct
D
45
E
36
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SOLUTION
Of the three-digit integers greater than 700, how many have two digits that are equal to each other and the remaining digit different from the other two?
Three-digit numbers can have only the following 3 patterns:
A. all digits are distinct;
B. two digits are alike and the third is different;
C. all three digits are alike.…
Of the three-digit integers greater than 700, how many have two digits that are equal to each other and the remaining digit different from the other two?
Three-digit numbers can have only the following 3 patterns:
A. all digits are distinct;
B. two digits are alike and the third is different;
C. all three digits are alike.…
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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