First slide

Theorems of probability

Question

Five different games are to be distributed among 4 children randomly. The probability that each child get at least one game is

Moderate

A

$\frac{1}{4}$
B

$\frac{15}{64}$
C

$\frac{21}{64}$
D

None of these

Solution

$Total number of ways of distribution is 4^{5}$
$∴ n (S) = 4^{5}$
Total number of ways of distribution so that each child gets at least one game is
$\begin{matrix} 4^{5} -^{4} C_{1} 3^{5} +^{4} C_{2} 2^{5} -^{4} C_{3} = 1024 - 4 \times 243 + 6 \times 32 - 4 \\ = n (E) = 240 \end{matrix}$
Therefore, the required probability is
$\frac{n (E)}{n (S)} = \frac{240}{4^{5}} = \frac{15}{64}$

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