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A box contains 20 balls, of which 5 are red, 5 are blue, 5 are white and 5 are green. Suppose a sample of 5 balls are chosen without replacement.

a) find the probability that the sample contains balls of all the same colour

(answer is 4/ 20C5, but why isnt it 5/20C5??)

b) find the probability that the sample contains three balls of one colour and two balls of another colour.

The teacher wrote

5C3 x 5C2 x 4P2

Could you please explain why this is?

  • maths -

    a) the ans. is 4/20C5 because there are 4 types of balls and 5 is the magnitude of a specific colour.
    b)5C3 gives value of 3 balls of 1 colour;
    5C2= value of 2 balls of another colour;
    4P2= probality of 2 colours from 4 colours ;
    20C5=combination of total balls of different colour.

  • maths -

    Dinga chika

  • maths -

    could be all red, all blue , all white or all green
    prob(all red) = (5/20)(4/19)(3/18)(2/17)(1/16) = /15504
    the same calculation for the others

    so the prob(all same colour) = 4(1/15504) = 1/3876
    which is the same as 4/C(20,5)

    Why isn't it 5/C(20,5) ??
    Why would it? There are only 4 colours

    3 colours of one kind, 2 of the others :
    BBBRR ...
    WWWRR ................
    There would be 12 of those

    let's look at one such case
    prob = C(5,3) x C(5,2)/C(20,5) = 10/15504
    but there are 12 cases with the same colour triple, and another colour double

    so prob = 12 x C(5,3) x C(5,2)/C(20,5)
    = 1200/15504
    = 25/323

    which is the same as your teacher's answer

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