# CAT Practice : Number System

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## Three digit number combinations

Q.11: How many 3-digit positive integers, with digits a, b and c exist such that a < b and c < b? Assume that a is in hundred's place, b is in ten's place, c is in unit's place and a is a non-zero digit.
1. 450
2. 240
3. 364
4. 648

Choice B. 240 numbers

## Detailed Solution

Given conditions are a < b and c < b

If b = 9, a can take any numbers between 1 and 8 and c can take any numbers between 0 and 8
Total combination of such numbers = 8 x 9 = 72

If b = 8, a can take any numbers between 1 and 7 and c can take any numbers between 0 and 7
Total combination of such numbers = 7 x 8 = 56

Similarly add all combinations till b = 1
= 8x9 + 7x8 + 6x7 + 5x6 + 4x5 + 3x4 + 2x3 + 1x2
= 240

Answer = 240 numbers are there

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