# Questionbank: Permutation and Probability

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Consider this - the digit can appear 1, 2 ir 3 times!!

## 3 Digit numbers > 500

Q.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

Choice B. 176

## Detailed Solution

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.

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