Question
Three numbers are chosen at random from 1 to 15. Probability that no two numbers are consecutive is
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Answers
R_scott
there are 15C2 pairs from 15 numbers ... (15 * 14) / (2 * 1) = 105
there are 14 consecutive pairs from 15 consecutive numbers
probability that a pair is NOT consecutive ... (105 - 14) / 105 = 91 / 105
three numbers is three distinct pairs
probability of no consecutive pairs in three numbers ... (91 / 105)^3
there are 14 consecutive pairs from 15 consecutive numbers
probability that a pair is NOT consecutive ... (105 - 14) / 105 = 91 / 105
three numbers is three distinct pairs
probability of no consecutive pairs in three numbers ... (91 / 105)^3