Question

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).

Answer 1

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.