# Questionbank: Permutation and Probability

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3 Digit numbers whose sum of the digits is less than 5 - Simple Counting

## 3 Digit Number - Sum of Digits

Q.25: Find all 3 digit numbers such that sum of their digits is a whole number less than 5.
1. 18
2. 20
3. 19
4. 17

Choice C. 13

## Detailed Solution

For the sum of the digits of a 3 digit number to be a whole number less than 5 – it can take the values – 0, 1 , 2, 3 or 4.

For sum =0, there are no such numbers.

Sum=1, Possible in 1 way(100).

Sum=2, Possible in 3 ways (110,101 and 200)

Sum=3, Possible in 6 ways (111, 210, 201, 120, 102 and 300)

Sum=4, Possible in 10 ways (121, 112, 211, 220, 202, 301, 310, 103, 130 and 400)

Total = 1+3+6+10 = 20 numbers are possible.

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