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## mathematics

### 1. Series 19. Year - S. probability

• Three cards are randomly selected from 36 cards. Calculate probability of possibility that (i) just one ace was selected, (ii) at least one ace is selected and (iii) no ace is selected.
• $N$ identical particles is in a container. Calculate probability of case, that in the left part of container is $m$ particles more than in the right half. Draw a graph of dependence for $N=10^{10}$. Range of $m$ select so that the probability on the sides will be one tenth of the probability in the middle. How the width depends on $N?$ (Width is difference $m_{2}-m_{1}$, where $m_{2}>0$ a $m_{1}<0$ are values of $m$, for which the probability is half compared to the maximum).
• Estimate size of ln$n!$ (without using Stirling formula).

Autor seriálu Matouš.