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?
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?"
Choice B is the correct answer.
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