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# GATE | GATE CS 2010 | Question 65

• Difficulty Level : Expert
• Last Updated : 28 Jun, 2021

Given digits 2, 2, 3, 3, 3, 4, 4, 4, 4 how many distinct 4 digit numbers greater than 3000 can be formed?
(A) 50
(B) 51
(C) 52
(D) 54

Explanation: First digit is either 3 or 4. We’ll consider each case separately:

(1) First digit is 3:
Then the rest of the numbers must come from the list: 2, 2, 3, 3, 4, 4, 4, 4
Therefore we may choose any 3-digit sequence except 222 and 333 for the rest of the digits. This shows there are
3*3*3 – 2 = 25
numbers in this case.

(2) First digit is 4:
Then the rest of the numbers must come from the list 2, 2, 3, 3, 3, 4, 4, 4
Therefore we may choose any 3-digit sequence except 222 for the rest of the digits. This shows there are
3*3*3 – 1 = 26
numbers in this case.

Now, the total number is just 25 + 26 = 51.

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