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  • Three numbers are chosen at random without replacement from . The probability th

Three numbers are chosen at random without replacement from 1,2,3, \ldots, 10. The probability that the minimum of the chosen numbers is 4 or their maximum is 8 , is

Option: 1

\frac{11}{40}


Option: 2

\frac{3}{10}


Option: 3

\frac{1}{40}


Option: 4

None of these


Answers (1)

best_answer

The probability of 4 being the minimum number \mathrm{=\frac{{ }^6 C_2}{{ }^{10} C_3}}

(because, after selecting 4 any two can be selected from 5, 6, 7, 8, 9, 10).

The probability of 8 being the maximum number \mathrm{=\frac{{ }^7 C_2}{{ }^{10} C_3}}

The probability of 4 being the minimum number and 8 being the maximum number \mathrm{=\frac{3}{{ }^{10} C_3}}

\mathrm{\therefore \text { the required probability }=P(A \cup B)=P(A)+P(B)-P(A \cap B)}

\mathrm{=\frac{{ }^6 C_2}{{ }^{10} C_3}+\frac{{ }^7 C_2}{{ }^{10} C_3}-\frac{3}{{ }^{10} C_3}=\frac{11}{40} .}

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Nehul

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