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  • 10 apples are distributed at random among 6 persons. The probability that at least one of them will receive none isOption: 1 <img alt="\frac{6}{143}"

10 apples are distributed at random among 6 persons. The probability that at least one of them will receive none is

Option: 1

\frac{6}{143}


Option: 2

\mathrm{\frac{{ }^{14} C_4}{{ }^{15} C_5}}


Option: 3

\frac{137}{143}


Option: 4

None of these


Answers (1)

best_answer

The required probability =1- probability of each receiving at least one

                                       \mathrm{=1-\frac{n(E)}{n(S)}}

Now , the number of integral solutions of \mathrm{x_1+x_2+x_3+x_4+x_5+x_6=10} such that \mathrm{x_1 \geq 1, x_2 \geq 1, \ldots, x_6 \geq 1} gives \mathrm{n(E)} and the number of integral solutions of \mathrm{x_1+x_2+\ldots+x_5+x_6=10} such that \mathrm{x_1 \geq 0, x_2 \geq 0, \ldots, x_6 \geq 0} gives \mathrm{n(S)}.

\therefore the required probability \mathrm{=1-\frac{{ }^{10-1} C_{6-1}}{{ }^{10+6-1} C_{6-1}}=1-\frac{{ }^9 C_5}{{ }^{15} C_5}=\frac{137}{143} \text {. }}

Posted by

Irshad Anwar

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