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A gardener has 13 identical looking tulip bulbs, of which 6 will produce yellow tulips and 7 will become pink. she randomly selects and plants 6 and gives the rest away. When the tulips start to bloom, what is the probability that all are yellow?

Answer :

Given data:

The total numbbers of bulbs are n=13.

The expression for the probability that gardener plants 6 yellow bulbs is,

[tex]\begin{gathered} P=\frac{6}{13}\times\frac{5}{12}\times\frac{4}{11}\times\frac{3}{10}\times\frac{2}{9}\times\frac{1}{8} \\ =\frac{1}{13\times11\times3\times4} \\ =\frac{1}{1716} \end{gathered}[/tex]

Thus, the probability that gardener plants 6 yellow bulbs is 1/1716.

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