Question

3 distinct numbers are chosen from the set {1,2,....6} the probability that the product of 2 numbers is the third one is

Answer 1

Answer:

$\red{ Probability } \green {= \frac{1}{20}}$

Step-by-step explanation:

$Given \: set \: {1,2,3,4,5,6}$

$Number \: of \: total \: possible \\outcomes = ^{6}C_{3}\\ = \frac{6!}{(6-3)! 3! } \\= \frac{6!}{3! 3!} \\= 20\:---(1)$

$Favourable \: outcomes = ( 2,3,6)$

$(i.e ., 2\times 3 = 6 )$

$Number \:of \: favourable \: outcomes = 1\:--(2)$

$Probability = \frac{(2)}{(1)}\\= \frac{1}{20}$

Therefore.,

$\red{ Probability } \green {= \frac{1}{20}}$

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