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In how many ways can 6 balls of different colours, namely black, white, blue, red, green and yellow be arranged in a row in such a way that the black and white balls ar never together? |
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Answer» Let us tie the black ball (b) and white ball (w) together and consider (bw) as one ball. Now, this (bw) and 4 other balls may be arranged in ` ""^(5)P_(5) =5! =120` ways. Also, these two balls may be arranged among themselves in `2! =2` ways. Total number of arrangements with black and white balls together `=(120xx2) =240.` Number of ways of arranging 6 balls among themselves `=""^(6)P_(6)=6! =720.` Number of ways of arranging 6 balls such that black and white balls are never together`=(720-240)=480.` |
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