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Question

# Three numbers are chosen at random withoutreplacement from the set of integers 1,2,3,....10. The probability that the minimum of the chosen numbers is 3 or the maximum of the chosen numbers is 7, is equal to

A
23/120
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B
13/120
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C
13/60
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D
11/40
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Solution

## The correct option is D 11/40Case 1: When 3 is minimumThen the number of choices for choosing 2 cards other then 7....4,5,6,8,9,10=6C2=15The number of ways when 7 is max but 3 not included: 1,2,4,5,6=10 waysWhen both 3,7 are present 8 waysTotal desired cases 33Total ways of picking 3 numbers at random =10C3=120Probability = 33/120=11/40

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