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  4. Four integers, from 0 to 9 inclusive written randomly. Probability that not more than two of them are alike, is

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Q. Four integers, from 0 to 9 inclusive written randomly. Probability that not more than two of them are alike, is

Probability - Part 2

Solution:

$ n ( S )=10^4$
$n ( A ) =10^4-(\text { exactly } 3 \text { alike }+1 \text { different }+ \text { all four alike }) $
$= 10^4-\left[{ }^{10} C _2 \cdot 2 ! \cdot \frac{4 !}{3 !}+10\right] $
image
$p = \frac{1000-37}{1000}=\frac{963}{1000}$