# CAT Quantitative Aptitude Questions | CAT Permutation and Combination Questions

###### CAT Questions | Permutation Probability | 3 Digit numbers > 500

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 33: How many 3-digit numbers greater than 500 contain the digit 9 appearing at least once?

1. 191
2. 176
3. 153
4. 189

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##### Method of solving this CAT Question from Permutation and Combination: Consider this - the digit can appear 1, 2 ir 3 times!!

509, 519... 999 all these numbers have atleast one 9 in them
These put together gives 50 numbers
Now 590,591,..599 atleast has one 9 , but 599 is already included in the first list. Hence 9 numbers.
Similarly for 600-900 series, all put together we get 45 numbers
All numbers from 900 to 999 have a 9 in them but 990-999 are already accounted and also 909,919..999 are accounted.

Hence 81 numbers will have 9 atleast once.
Put together totally 176 numbers have atleast one 9 in them between 500-999.

The question is "How many 3-digit numbers greater than 500 contain the digit 9 appearing at least once?"

##### Hence the answer is "176"

Choice B is the correct answer.

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