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The number of functions f from {1, 2, 3,...., 20} onto (1, 2, 3,...., 20)} such that f(k) is a multiple of 3, whenever k is a multiple of 4, is : (1) 65 x (15)!(2) 5! x 6! (3) 56 x 15 (4) (15)! x 6! |
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Answer» Correct option (4) (15)! × 6! Explanation: f(k) = (3, 6, 9, 12, 15, 18) For k = 4, 8, 12, 16, 20 For these k we have 6.5.4, 3.2 ways = 6! For other numbers we have 15! ways. So total = 15!.6! |
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