Probability of drawing three balls of white colour

Question

A bag contains 5 White,7 black, 4 Red balls. Find the probability that three balls drawn at random are white.

My attempt:

The sample space for drawing 3 balls is {WWW,BBB,RRR,WBB,WRR,RBB,RWW,BRR,BWW}. So required probability is 1/9. But answer given is 1/56. Where am I wrong?

Answer 1

In total, there are 16 balls and you need the probability of picking 3 white balls. You can consider 3 different cases each time you pick a ball, and then multiply the probabilities to get the desired answer.

Pick 1:
Total balls: 16
White balls: 5
Probability of picking white P(w): $5\over16$

Pick 2:
Total: 15
White: 4
P(w): $4\over15$

Pick 2:
Total: 14
White: 3
P(w): $3\over14$

Now that you have got the individual probabilities, the total probability of drawing 3 white balls is: $P(3W)=P(\text{W in Pick 1})\times P(\text{W in Pick 2})\times P(\text{W in Pick 3})=\Large\frac{5}{16}\times \frac{4}{15}\times \frac{3}{14}=\frac{1}{56}$