A bag contains 5 blue balls, 4 black balls and 3 red balls. Six balls are drawn at random. What is the probability that there are equal numbers of balls of each color?

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Solution

Total number of ways for selecting 6 balls = $^{12} C$ $_{6}$
Total no. of ways of selcting 6 balls such that equal no. of balls of each color occur = $^{5} C$ $_{2}$ $\times$ $^{4} C$ $_{2}$ $\times$ $^{3} C$ $_{2}$
So, Probablity of picking equal no. of balls of each color = $\frac{15}{77}$

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A bag contains 5 blue balls, 4 black balls and 3 red balls. Six balls are drawn at random. What is the probability that there are equal numbers of balls of each color?

Total number of ways for selecting 6 balls = 12C 6Total no. of ways of selcting 6 balls such that equal no. of balls of each color occur = 5C 2 × 4C 2 × 3C 2So, Probablity of picking equal no. of balls of each color = 1577

Total number of ways for selecting 6 balls = $^{12} C$ $_{6}$
Total no. of ways of selcting 6 balls such that equal no. of balls of each color occur = $^{5} C$ $_{2}$ $\times$ $^{4} C$ $_{2}$ $\times$ $^{3} C$ $_{2}$
So, Probablity of picking equal no. of balls of each color = $\frac{15}{77}$