Latest gate Aptitude Question SOLUTION: Q. Given digits 2, 2, 3, 3, 3, 4, 4, 4, 4, how many distinct 4 digit numbers greater than 3000 can be formed?

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Q. Given digits 2, 2, 3, 3, 3, 4, 4, 4, 4, how many distinct 4 digit numbers greater than 3000 can be formed?

Asked In gate Mareesh janadri (10 years ago)

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BISWAJIT  (10 years ago)

As our four digit numbers have to be greater than 3000, so we have only two options -- the numbers will start with 3 or 4.

CASE 1: (Format of the no. is 3 * * *)
Now we have the digits 2, 2, 3, 3, 4, 4, 4, 4
Now if we consider that there are one 2 and one 3 more, then the blank spaces could be filled up in 3X3X3 ways, i.e. in 27 ways.
But we have two options less, as we cannot form 3222 and 3333.
So in this case, total no. of numbers is (27 - 2) = 25.

CASE 2:(Format of the no. is 4 * * *)
Now we have the digits 2, 2, 3, 3, 3, 4, 4, 4
Now if we consider that there is one 2 more, then the blank spaces could be filled up in 3X3X3 ways, i.e. in 27 ways.
But we have one options less, as we cannot form 4222.
So in this case, total no. of numbers is (27 - 1) = 26.

Here from the above two cases, we see that there are (25 + 26) = 51such numbers.

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