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In how many ways we can arrange 3red flowers, 4 yellow flowers and 5 white flowers in a row. In how many ways this is possible if the white flowers are to be separated in any arrangement (Flowers of same colour are identical). |
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Answer» Total we have 12 flowers 3 red, 4 yellow and 5 white. Number of arrangements = 12!/3!4!5! = 27720. For the second part, first arrange 3 red & 4 yellow. This can be done in = 7!/3!4! = 35 ways. Now select 5 places from among 8 places (including extremes) & put the white flowers there. This can be done in 8C5 = 56. ∴ The number of ways for the 2nd part = 35 × 56 = 1960. |
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