Question 47

A box contains 10 balls out of which 3 are red and the rest are blue. In how many ways can a random sample of 6 balls be drawn from the bag so that at the most 2 red balls are included in the sample and no sample has all the 6 balls of the same colour?

Solution

Six balls can be selected in the following ways : (1 red ball and 5 blue balls) or (2 red balls and 4 blue balls)

Since, all the six balls cannot be blue.

=> Total number of ways = $$(C^3_1\times C^7_5)+(C^3_2\times C^7_4)$$

= $$(3\times21)+(3\times35)$$

= $$63+105=168$$

=> Ans - (B)


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