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  • 10 different books and 2 different pens are given to 3 boys so that each gets equal number of things. The probability that the same boy does not receive both the pens is

10 different books and 2 different pens are given to 3 boys so that each gets equal number of things. The probability that the same boy does not receive both the pens is

Option: 1

\frac{5}{11}


Option: 2

\frac{7}{11}


Option: 3

\frac{2}{3}


Option: 4

\frac{6}{11}


Answers (1)

best_answer

\mathrm{n(S)={ }^{12} C_4 \times{ }^8 C_4 \times{ }^4 C_4 .}

\mathrm{n(E)=n(S)-} the number of ways in which one boy gets both the pens

            \begin{aligned} & =\mathrm{n(S)-{ }^{10} C_2 \times{ }^8 C_4 \times{ }^4 C_4 \times(3 !)} \\ \\\therefore & \: \: \mathrm{P(E)=1-\frac{{ }^{10} C_2 \times{ }^8 C_4 \times{ }^4 C_4 \times(3 !)}{{ }^{12} C_4 \times{ }^8 C_4 \times{ }^4 C_4}=1-\frac{6}{11}=\frac{5}{11}.} \end{aligned}

Posted by

vishal kumar

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