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Math Help - Classical definition of probability

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    Senior Member pankaj's Avatar
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    Classical definition of probability

    Two numbers x and y are chosen from the set \{1,2,3.....,5n\}. Find the probability that x^4+y^4 is divisible by 5.
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    Moo
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    Hello,
    Quote Originally Posted by pankaj View Post
    Two numbers x and y are chosen from the set \{1,2,3.....,5n\}. Find the probability that x^4+y^4 is divisible by 5.
    Note that (5k+r)^4 with r \in \{1,2,3,4\} has a remainder 1 in the division by 5.

    Therefore, none of these numbers 5k+r would be such that x^4+y^4 is divisible by 5.

    Remain the multiples of 5. There are n of them in the set. How many ways are there to choose 2 objects randomly among n ? (with replacement)
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