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GATE | GATE CS 2010 | Question 65

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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

Answer: (B)

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. Source: http://in.answers.yahoo.com/question/index?qid=20100216113008AANZGwP

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Last Updated : 28 Jun, 2021
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