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Mathematics - Permutation & Combination Question with Solution | TestHub

MathematicsPermutation & CombinationGroup formationMedium2 minQB

MathematicsMediumsingle choice

5 different marbles are placed in 5 different boxes randomly. Find the probability that exactly 2 boxes remain empty, given that each box can hold any number of marbles

Options:

Answer:

Solution:

2 empty boxes can be selected in $^{5} C_{2}$ ways and 5 marbles can be placed in remaining 3

boxes in groups of 221 or 311 in $3! (\frac{5 !}{2 ! 2 ! 2 !} + \frac{5 !}{3 ! 2 !}) = 150$

Stream:JEESubject:MathematicsTopic:Permutation & CombinationSubtopic:Group formation

⏱ 2mℹ️ Source: QB

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