Mathematics - Probability Question with Solution | TestHub

MathematicsProbabilityGeneral (Event SS, Definitions, Odd against/Favour)Hard2 minQB

MathematicsHardsingle choice

Six fair dice are thrown independently .The probability that there are exactly 2 different pairs (A pair is an ordered combination like 2, 2, 1, 3, 5, 6) is

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Answer:

Solution:

Total no. of outcomes $= 6^{6}$ . number of ways of choosing 4 other different numbers is $6_{C_{2}}$ and choosing 2 out of remaining 4 can be lone in $^{4} C_{2}$ ways. Also number of ways of arranging 6 numbers of which 2 are alike and 2 are alike is $\frac{6}{2 ! 2 !}$ .

$∴ Required probability = \frac{6 _{C_{2}} \times 4 _{C_{2}} \times \frac{6}{2 ! 2 !}}{6 ^{6}} = \frac{25}{72} .$

Stream:JEESubject:MathematicsTopic:ProbabilitySubtopic:General (Event SS, Definitions, Odd against/Favour)

⏱ 2mℹ️ Source: QB

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