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# In a physics degree course, there is an average dropout of 17 students in the first semester. What is the probability that the number of dropouts in the first semester in a randomly selected year has between 13 and 16 students?

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## Answer to a math question In a physics degree course, there is an average dropout of 17 students in the first semester. What is the probability that the number of dropouts in the first semester in a randomly selected year has between 13 and 16 students?

Esmeralda
4.7
$\frac{ {17}^{13} }{ 13 ! \times {e}^{17} }+\frac{ {e}^{-17} \times {17}^{14} }{ 14 ! }+\frac{ {e}^{-17} \times {17}^{15} }{ 15 ! }+\frac{ {e}^{-17} \times {17}^{16} }{ 16 ! }$
$\frac{ {17}^{13} }{ 13 ! \times {e}^{17} }+\frac{ {17}^{14} }{ 14 ! \times {e}^{17} }+\frac{ {e}^{-17} \times {17}^{15} }{ 15 ! }+\frac{ {e}^{-17} \times {17}^{16} }{ 16 ! }$
$\frac{ {17}^{13} }{ 13 ! \times {e}^{17} }+\frac{ {17}^{14} }{ 14 ! \times {e}^{17} }+\frac{ {17}^{15} }{ 15 ! \times {e}^{17} }+\frac{ {e}^{-17} \times {17}^{16} }{ 16 ! }$
$\frac{ {17}^{13} }{ 13 ! \times {e}^{17} }+\frac{ {17}^{14} }{ 14 ! \times {e}^{17} }+\frac{ {17}^{15} }{ 15 ! \times {e}^{17} }+\frac{ {17}^{16} }{ 16 ! \times {e}^{17} }$
$\frac{ {17}^{13} }{ 13 ! \times {e}^{17} }+\frac{ {17}^{14} }{ 14 \times 13 ! \times {e}^{17} }+\frac{ {17}^{15} }{ 15 ! \times {e}^{17} }+\frac{ {17}^{16} }{ 16 ! \times {e}^{17} }$
$\frac{ {17}^{13} }{ 13 ! \times {e}^{17} }+\frac{ {17}^{14} }{ 14 \times 13 ! \times {e}^{17} }+\frac{ {17}^{15} }{ 15 \times 14 \times 13 ! \times {e}^{17} }+\frac{ {17}^{16} }{ 16 ! \times {e}^{17} }$
$\frac{ 14 \times 15 \times 16 ! \times {17}^{13}+15 \times 16 ! \times {17}^{14}+16 ! \times {17}^{15}+14 \times 15 \times 13 ! \times {17}^{16} }{ 14 \times 15 \times 13 ! \times {e}^{17} \times 16 ! }$
$\frac{ 210 \times 16 ! \times {17}^{13}+15 \times 16 ! \times {17}^{14}+16 ! \times {17}^{15}+14 \times 15 \times 13 ! \times {17}^{16} }{ 14 \times 15 \times 13 ! \times {e}^{17} \times 16 ! }$
$\frac{ 210 \times 16 ! \times {17}^{13}+15 \times 20922789888000 \times {17}^{14}+16 ! \times {17}^{15}+14 \times 15 \times 13 ! \times {17}^{16} }{ 14 \times 15 \times 13 ! \times {e}^{17} \times 16 ! }$
$\frac{ 210 \times 16 ! \times {17}^{13}+15 \times 20922789888000 \times {17}^{14}+20922789888000 \times {17}^{15}+14 \times 15 \times 13 ! \times {17}^{16} }{ 14 \times 15 \times 13 ! \times {e}^{17} \times 16 ! }$
$\frac{ 210 \times 16 ! \times {17}^{13}+15 \times 20922789888000 \times {17}^{14}+20922789888000 \times {17}^{15}+\left$13 ! \times 14 \times 15 \right$ \times {17}^{16} }{ 14 \times 15 \times 13 ! \times {e}^{17} \times 16 ! }$
$\frac{ 210 \times 16 ! \times {17}^{13}+15 \times 20922789888000 \times {17}^{14}+20922789888000 \times {17}^{15}+\left$13 ! \times 14 \times 15 \right$ \times {17}^{16} }{ \left$13 ! \times 14 \times 15 \right$ \times 16 ! \times {e}^{17} }$
$\frac{ 210 \times 20922789888000 \times {17}^{13}+15 \times 20922789888000 \times {17}^{14}+20922789888000 \times {17}^{15}+\left$13 ! \times 14 \times 15 \right$ \times {17}^{16} }{ \left$13 ! \times 14 \times 15 \right$ \times 16 ! \times {e}^{17} }$
$\frac{ 210 \times 20922789888000 \times {17}^{13}+15 \times 20922789888000 \times {17}^{14}+20922789888000 \times {17}^{15}+15 ! \times {17}^{16} }{ \left$13 ! \times 14 \times 15 \right$ \times 16 ! \times {e}^{17} }$
$\frac{ 210 \times 20922789888000 \times {17}^{13}+15 \times 20922789888000 \times {17}^{14}+20922789888000 \times {17}^{15}+15 ! \times {17}^{16} }{ 15 ! \times 16 ! \times {e}^{17} }$
$\frac{ 210 \times 20922789888000 \times {17}^{13}+15 \times 20922789888000 \times {17}^{14}+20922789888000 \times {17}^{15}+1307674368000 \times {17}^{16} }{ 15 ! \times 16 ! \times {e}^{17} }$
$\frac{ 210 \times 20922789888000 \times {17}^{13}+15 \times 20922789888000 \times {17}^{14}+20922789888000 \times {17}^{15}+1307674368000 \times {17}^{16} }{ 1307674368000 \times 16 ! \times {e}^{17} }$
$\frac{ \left$210 \times 20922789888000+15 \times 20922789888000 \times 17+20922789888000 \times {17}^{2}+1307674368000 \times {17}^{3} \right$ \times {17}^{13} }{ 1307674368000 \times 16 ! \times {e}^{17} }$
$\frac{ \left$4393785876480000+15 \times 20922789888000 \times 17+20922789888000 \times {17}^{2}+1307674368000 \times {17}^{3} \right$ \times {17}^{13} }{ 1307674368000 \times 16 ! \times {e}^{17} }$
$\frac{ \left$4393785876480000+5335311421440000+20922789888000 \times {17}^{2}+1307674368000 \times {17}^{3} \right$ \times {17}^{13} }{ 1307674368000 \times 16 ! \times {e}^{17} }$
$\frac{ \left$4393785876480000+5335311421440000+20922789888000 \times 289+1307674368000 \times {17}^{3} \right$ \times {17}^{13} }{ 1307674368000 \times 16 ! \times {e}^{17} }$
$\frac{ \left$4393785876480000+5335311421440000+20922789888000 \times 289+1307674368000 \times 4913 \right$ \times {17}^{13} }{ 1307674368000 \times 16 ! \times {e}^{17} }$
$\frac{ \left$9729097297920000+20922789888000 \times 289+1307674368000 \times 4913 \right$ \times {17}^{13} }{ 1307674368000 \times 16 ! \times {e}^{17} }$
$\frac{ \left$9729097297920000+6046686277632000+1307674368000 \times 4913 \right$ \times {17}^{13} }{ 1307674368000 \times 16 ! \times {e}^{17} }$
$\frac{ \left$9729097297920000+6046686277632000+6424604169984000 \right$ \times {17}^{13} }{ 1307674368000 \times 16 ! \times {e}^{17} }$
$\frac{ \left$15775783575552000+6424604169984000 \right$ \times {17}^{13} }{ 1307674368000 \times 16 ! \times {e}^{17} }$
$\frac{ 22200387745536000 \times {17}^{13} }{ 1307674368000 \times 16 ! \times {e}^{17} }$
$\frac{ 16977 \times {17}^{13} }{ 16 ! \times {e}^{17} }$
$\frac{ 16977 \times {17}^{13} }{ 20922789888000{e}^{17} }$
\begin{align*}&\frac{ 5659 \times {17}^{13} }{ 6974263296000{e}^{17} } \\&\approx0.332714\end{align*}

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