JEE Advance - Mathematics (2009 - Paper 1 Offline - No. 14)
The number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only, is
55
66
77
88
Explanation
The two possible cases are as follows:
Case 1 : There are five 1's; one 2; one 3. Therefore, the number of numbers is 7!/5! = 42.
Case 2 : There are four 1's; three 2's. Therefore, the number of numbers is 7!/4! 3! = 35. Hence, the total number of numbers is 42 + 35 = 77
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