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Probability - Gravner-55

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An urn contains $20$ balls numbers $1,.........20$. Select $5$ balls at random, without replacement. Let X be the largest number among selected balls. Determine its p.m.f. and the probability that at least one the selected numbers is $15$ or more.
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probability that at least one the selected numbers is 15 or more

= 1 - ( probability of selecting 5 numbers from 1...14) = 1 - (none of the numbers selected from 15...20)

= 1 - ($\frac{14C_5}{20C_5}$)
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