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  • Three numbers are chosen at random without replacement from the set <img alt="\mathrm{A=\{x \mid 1 \leq x \leq 10, x \in N\}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7BA%3D%

Three numbers are chosen at random without replacement from the set \mathrm{A=\{x \mid 1 \leq x \leq 10, x \in N\}}. The probability that the minimum of the chosen numbers is 3 and maximum is 7 , is

Option: 1

\frac{1}{12}


Option: 2

\frac{1}{15}


Option: 3

\frac{1}{40}


Option: 4

None of these


Answers (1)

best_answer

\mathrm{n(S)={ }^{10} C_3 } and 

\mathrm{n(E)={ }^3 C_1}, because on selecting 3,7 and we have to select one from 4,5 and 6.

\mathrm{\therefore \quad P(E)=\frac{{ }^3 C_1}{{ }^{10} C_3}=\frac{1}{40}}

Posted by

Suraj Bhandari

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