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A box contains 55 balls numbered from 1 to 55. If 8 balls are drawn with replacement, what is the probability that at least two of them have the same number?

  • Discrete Math - , Wednesday, April 27, 2011 at 4:04pm

    Number of (ordered) ways to draw 8 balls with replacement
    = 55^8
    Number of ways to draw 8 different balls
    =55P8
    = 55!/47!

    Probability of drawing 8 balls with at least two having the same number
    = 1-(55!/47!)/55^8
    = 25193936479/60897409375
    = 0.414 approx.

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