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Question

There are 5 white,4 yellow,3 green,2 blue and 1 red balls. All the balls are identical except for the color. These are to be arranged in a line in 5 places. Find the number of distinct arrangements.

A
2322
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B
5230
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C
1244
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D
2111
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Solution

The correct option is B 2111
5 White
4 Yellow
2 Blue
1 Red
Cases
(1) All are diffrent
(2) A pair and 3 diffrent
(3) 2 Pair of diffrent colors and 1 diffrent colour
(4) A pair and triad of diffrent colours
(5) A triad of 1 colour and 2 singles of diffrent colours
(6) A quad of single colour and a singles of another colour
(7) All five balls of same colour
(1)+(2)+(3)+(4)+(5)+(6)+(7)
5!+4C1×4C3×5!2!+4C2×3C1×5!2!×2!+(3C1)2×5!2!×3!+3C1×4C2×5!2!+2C1×4C1×5!2!+1
=2111

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