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There are unlimited number of identical balls of four different colours. How many arrangements of at most 8 balls in row can be made by using them?A. 21845B. 87380C. 262140D. none of these

Answer» Since there are balls of four different colours. Therefore,
Number of arrangements of one ball =4
Number of arrangements of two balls `=4xx4=4^(2)`
Number of arrangements of three balls `=4xx4xx4=4^(3)` etc.
`:.` Required number of arrangements
`=4+4^(2)+4^(3)+......+4^(8)`
`=4((4^(8)-1)/(4-1))=(4)/(3)(4^(8-1))=87380`


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