From the integers 110 four numbers are chosen at random with

From the integers 1,...,10, four numbers are chosen at random without replacement. What is the probability that the smalllest number is 3 and the largest is 7?

Solution

you have 10 posibilities that you can choose ( from 1 to 10)

for the smallest number will be 3 you just have 4,5,6,7,8,9,10 that can be more bigger than 3

you have 7 posibilities (favorables cases)

Probability will be = (7C4) / (10C4) = 35/210 = 0.1667

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probability that the largest is 7

you have 1,2,3,4,5,6 that are small than 7 you have 6 posibilities to choose

Probability = ( 6C4 ) / (10C4 ) = 15/210 = 0.0714