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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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