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.
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 :
RRRBB RRRWW RRRGG
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)
which is the same as your teacher's answer
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