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Mathematics (Mixed)
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The number 2006 is made up of exactly two zeros and two other digits whose sum is 8. What is the number of 4 digit numbers with these properties (including 2006)?
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A
21
💡 Explanation:
Since it is a 4 digit number, first digit cannot be 0.
Case 1: (When 0's are at 3rd and 4th place)
Possible cases are (7,1), (6,2), (5,3), (4,4), (3,5), (2,6), (1.7), i.e. there are 7 possible cases.
Similar cases are possible for CASE 2: (When 0's lie at 2nd and 3rd place).
Similarly, there are 7 possible cases for CASE3 (When 0's lie at 2nd and 4th place).
Total number of cases is 21. Hence, this is the correct option.