First slide

Introduction to probability

Question

Five different games are to be distributed among four children randomly. The probability that each child get at least one game is p, then the value of [1/p] is, where [.] represents the greatest integer function, _________.

Moderate

Solution

Total ways of distribution = n(S) = 4⁵
Total ways of distribution so that each child get at least one game
$\begin{matrix} n (E) = 4^{5} -^{4} C_{1} 3^{5} +^{4} C_{2} 2^{5} -^{4} C_{3} \\ = 1024 - 4 \times 243 + 6 \times 32 - 4 \\ = 240 \end{matrix}$
Required probability $p = \frac{n (E)}{n (S)} = \frac{240}{4^{5}} = \frac{15}{64}$

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