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?

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Answer 1 · 2017-08-02T13:05:13

The probability is $=0.0126$

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

$P=(120xx84xx35)/(28048800)=352800/28048800=0.0126$