There is 16 white, 9 red and 7 yellow tulips. What's the probability of randomly picking 9 flowers where 2 are white, 3 are red, and 4 are yellow?

Aug 2, 2017

The probability is $= 0.0126$

Explanation:

The probability of an event $A$ is

${P}_{A} =$(number of favourable outcomes)$/$total number of possibilities

Total number of tulips $= 16 + 9 + 7 = 32$

Number of ways of choosing $9$ tulips from $32$ is

Omega=((32),(9))=(32!)/(9!xx21!)=28048800

Number of ways of choosing $2$ white tulips from $16$ is

W=((16),(2))=(16!)/(2!xx14!)=120

Number of ways of choosing $3$ red tulips from $9$ is

R=((9),(3))=(9!)/(3!xx9!)=84

Number of ways of choosing $4$ yellow tulips from $7$ is

Y=((7),(4))=(7!)/(4!xx3!)=35

Probability is

$P = \frac{120 \times 84 \times 35}{28048800} = \frac{352800}{28048800} = 0.0126$