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There are unlimited number of identical balls of four different colours. The number of arrangement of atmost 8 balls in a row that can be made by using them is

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Detailed Solution

$4^{1} + 4^{2} + \dots + 4^{8} = \frac{4}{3} (4^{8} - 1) = 87380$

1 ball arrangement = 4 ways
2 ball arrangement =4×4 ways
3 ball arrangement =4×4×4 ways……

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