# CAT Quantitative Aptitude Questions | CAT Permutation and Combination Questions

###### CAT Questions | Permutation Probability | Sum of Digits CAT Questions

The question is from Permutation and Combination. Another question which combines number theory with combinatorics. Our task is to find number of 3 digits numbers which satisfies the given condition. This section hosts a number of questions which are on par with CAT questions in difficulty on CAT Permutation and Combination, and CAT Probability.

Question 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

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##### Method of solving this CAT Question from Permutation and Combination: 3 Digit numbers whose sum of the digits is less than 5 - Simple Counting

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.

The question is "Find all 3 digit numbers such that sum of their digits is a whole number less than 5?"

##### Hence the answer is "20"

Choice B is the correct answer.

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