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Q.

There are 6 balls of each of the four colours: red, white, yellow and black in a bag (balls of same colour are identical). Let n be the total number of different ways of drawing 6 balls one by one without replacement such that no two consecutive balls are of the same colour and no colour is missing in the draw. Find the non–zero digit in n.

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answer is 6.

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Detailed Solution

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$n = 4 \times 3^{5} - {}^{4}C_{1} {.3.2}^{5} + {}^{4}C_{2} {.2.1}^{5} = 600$

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There are 6 balls of each of the four colours: red, white, yellow and black in a bag (balls of same colour are identical). Let n be the total number of different ways of drawing 6 balls one by one without replacement such that no two consecutive balls are of the same colour and no colour is missing in the draw. Find the non–zero digit in n.