A bag contains 3 White, 3 black and 2 red balls. One by one three balls are drawn without replacement. Find the probability that third ballis red

Explanation

Let R for red ball, B for ball, and W for white ball.

Then, the required probability `=P(W W R)+P(B B R)+P(W B R)+P(B W R)+ P(W R R)+P(B R R)+P(R W R)+P(R B R)`
`


=frac{3 times 2 times 2}{8 times 7 times 6}+frac{3 times 2 times 2}{8 times 7 times 6}+frac{3 times 3 times 2}{8 times 7 times 6}+frac{3 times 3 times 2}{8 times 7 times 6}+frac{3 times 2 times 1}{8 times 7 times 6}+frac{3 times 2 times 1}{8 times 7 times 6}+
frac{2 times 3 times 1}{8 times 7 times 6}+frac{2 times 3 times 1}{8 times 7 times 6} `
`
=frac{2}{56}+frac{2}{56}+frac{3}{56}+frac{3}{56}+frac{1}{56}+frac{1}{56}+frac{1}{56}+frac{1}{56}=frac{1}{4}`