This used binomial probability.Originally Posted byskhan

Over here you need all 5 not to. The probability of that not happening is 90% thus,

Originally Posted byskhan

Here you have 25 of them, thus you need to find,Originally Posted byskhan

This is probability of two events. First find between 3 and 6 which is,Originally Posted byskhan

And then probability exactly 4 which is,

Now multiply them to get,

.

Credits

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CaptainBlack for the nice trick for combinations using LaTeX really helped.