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Class 11MathematicsPermutations and CombinationsCombinationsExpert
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From (9) distinct books and (4) identical magazines, (6) objects are to be selected with at least (2) magazines. How many selections are possible?

Answer and explanation

Correct answer: (246)

The direct answer is option C, 246. The 4 magazines are identical, so choosing 2 magazines is only one magazine-choice pattern, not \(^{4}C_2\). The 9 books are distinct, so their choices are counted with combinations. At least 2 magazines means the number of magazines can be 2, 3, or 4. If 2 magazines are selected, 4 books must be selected: \(^{9}C_4=126\). If 3 magazines are selected, 3 books are selected: \(^{9}C_3=84\). If 4 magazines are selected, 2 books are selected: \(^{9}C_2=36\). Adding disjoint cases gives \(126+84+36=246\). Option A, 210, misses or miscounts a case. Option B, 228, is not the correct sum. Option C, 246, includes exactly all three allowed magazine cases. Option D, 264, overcounts. The key lesson is that identical objects do not create separate choices by identity, while distinct books do.

Related tags

Identical-MagazinesAtleastCombinations
सुधार सुझाएँ / Earn

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