Question

Find the probability

A bag contains five red balls and four white balls, if three balls are removed from the bag, that:
a) they are all red;
b) two are red, one white;
c) they are all white;
d) two are white, one red;

I try to use nCr/nPr but seems getting the different answer to the solution, eg in a). if I use nCr (n=5, r =3) I got 10 which is correct, however for nPr (n = 9, r = 3) i didn't get 84. instead I got 504. the solution I have been given is nCr = 5 / nPr = 42.

Answer 1

This is sampling without replacement (order not important - Hence use combination nCr not nPr)

The bag contains five red balls and four white balls. 3 balls are removed from the bag. The number of ways of choosing 3 balls from 5+4=9 balls is .

a) The probability that they are all red is

b) The probability that two are red, one white is

c) The probability that they are all white is

d) The probability that two are white, one red