Three numbers are chosen at random from 1 to 15. The probability that no two numbers are consecutive is
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Three numbers are chosen at random from 1 to 15. Probability that all three numbers are not consecutive = 34/35
Step-by-step explanation:
Consecutive numbers can be
(1,2 ,3) , (2,3,4) , (3,4,5) , (4,5,6) ,(5,6,7) , (6,7,8) , (7,8,9) , (8,9,10) ,(9,10,11) , (10,11,12) ,(11,12,13) , (12,13,14) & (13,14,15)
13 Combination
and each combination can be 3 * 2 * 1 = 6 ways
total possible = 13 * 6 = 78
Total Combinations = 15 * 14 * 13 = 2730
Probability = 78 / 2730 = 1/35
Probability that all three numbers are not consecutive = 1 - 1/35
= 34/35
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