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  • Fifteen football players of a club-team are given  T-shirts with their names written on the backside. If the players pi

Fifteen football players of a club-team are given 15 T-shirts with their names written on the backside. If the players pick up the T-shirts randomly, then the probability that at least 3 players pick the correct T-shirt is

Option: 1

\frac{5}{24}


Option: 2

\frac{1}{6}


Option: 3

\frac{5}{36}


Option: 4

\frac{2}{15}


Answers (1)

best_answer

\mathrm{Required \: probability =1-\frac{D_{\left ( 15 \right )}+^{15}C_{1}D_{\left ( 14 \right )}+^{15}C_{2}D_{(3)}}{15!}}

\mathrm{Taking \: D_{(15)}\: as\: \frac{15!}{e}}

\mathrm{D_{(14)}\: as\: \frac{14!}{e}}

\mathrm{D_{(13)}\: as\: \frac{13!}{e}}

\begin{aligned} & \text { We get } 1-\left(\frac{\frac{15 !}{\mathrm{e}}+15 \frac{14 !}{\mathrm{e}}+\frac{15 \times 14}{2 \times 1} \times \frac{13 !}{\mathrm{e}}}{15 !}\right) \\ \end{aligned}

\begin{aligned} & =1-\left(\frac{1}{\mathrm{e}}+\frac{1}{\mathrm{e}}+\frac{1}{2 \mathrm{e}}\right)=1-\frac{5}{2 \mathrm{e}} \simeq 0.08 \end{aligned}

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