Mathematics - Permutation & Combination Question with Solution | TestHub

MathematicsPermutation & CombinationnPr & nCrHard2 minPYQ_2024

MathematicsHardsingle choice

The number of arrangements of all digits of 12345 such that at least 3 digits will not come in its position is

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Answer:

Solution:

Total number of ways such that at least 3 digits will not come in its position $=^{5} C_{3} {3! -^{3} C_{1} 2! +^{3} C_{2} 1! -^{3} C_{3} 0!}$ $+^{5} C_{4} {4! -^{4} C_{1} (3!) +^{4} C_{2} (2!) -^{4} C_{3} (1!) +^{4} C_{4} (0!)}$ $+^{5} C_{4} {5! -^{5} C_{1} 4! +^{5} C_{7} 3! -^{5} C_{2} 2! +^{5} C_{4} 1! -^{5} C_{5} (0!)}$ $= 10 (2) + 5 (9) + (44) = 20 + 45 + 44 = 109$

Stream:BITSATSubject:MathematicsTopic:Permutation & CombinationSubtopic:nPr & nCr

⏱ 2mℹ️ Source: PYQ_2024

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