Question:
Three numbers are randomly picked from the set \(\{0,1,2,3,4,5,6,7,8,9\}\) one after another without replacement. If p be the probability that the smallest of these three numbers is less than 4, then 18p is equal to ________.
Three numbers are randomly picked from the set \(\{0,1,2,3,4,5,6,7,8,9\}\) one after another without replacement. If p be the probability that the smallest of these three numbers is less than 4, then 18p is equal to ________.
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Use the complement: the smallest is not less than 4 exactly when all three numbers come from \(\{4,5,\dots,9\}\).
Updated On: Nov 12, 2026
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Correct Answer: 15
Solution and Explanation
Total ways of choosing 3 numbers out of 10: \(\binom{10}{3}=120\) (order does not affect the smallest number).
The smallest number is at least 4 when all three come from \(\{4,5,6,7,8,9\}\): \(\binom63=20\) ways.
\(p=1-\frac{20}{120}=\frac56\).
\(18p=18\times\frac56=15\).
Answer: 15
The smallest number is at least 4 when all three come from \(\{4,5,6,7,8,9\}\): \(\binom63=20\) ways.
\(p=1-\frac{20}{120}=\frac56\).
\(18p=18\times\frac56=15\).
Answer: 15
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