# Exercise ID387

Probability and Statistics → Probability → Probability and combinatorial methods
[Level: ] [Number of helps: 1] [Number of pictures: 0] [Number of steps: 7] [Number of characters: 81]

The class organizes a lottery with three numbers from numbers: 1, 2, 3, 4, 5 . Tom markes 2, 3 and 5 number on the coupon.
Calculate the probability that Tom will have a total win!

$P\left(A\right)=\frac{\left|A\right|}{\left|\Omega \right|}\phantom{\rule{0ex}{0ex}}$ $\phantom{\rule{0ex}{0ex}}$$\left|\Omega \right|={C}_{3}^{5}=\left(\begin{array}{c}5\\ 3\end{array}\right)\phantom{\rule{0ex}{0ex}}$ $\phantom{\rule{0ex}{0ex}}$$\left|\Omega \right|=\left(\begin{array}{c}5\\ 3\end{array}\right)=\frac{5·4·3}{3!}=\frac{5·4·{3}}{{3}·2·1}=5·2\phantom{\rule{0ex}{0ex}}$ $\phantom{\rule{0ex}{0ex}}$$\left|\Omega \right|=10\phantom{\rule{0ex}{0ex}}$ $\phantom{\rule{0ex}{0ex}}$$\left|A\right|=1\phantom{\rule{0ex}{0ex}}$ $\phantom{\rule{0ex}{0ex}}$$P\left(A\right)=\frac{\left|A\right|}{\left|\Omega \right|}=\frac{1}{10}\phantom{\rule{0ex}{0ex}}$ $\phantom{\rule{0ex}{0ex}}$$P\left(A\right)=0,1\phantom{\rule{0ex}{0ex}}$
HELP AVAILABLE!
$P\left(A\right)=0,1$

$P\left(A\right)=\frac{\left|A\right|}{\left|\Omega \right|}$

${C}_{k}^{n}=\left(\begin{array}{c}n\\ k\end{array}\right)$