Question

How many decorations are there using 12 blue balloons, 9 green lanterns and 6 red ribbons ina row, such that no two ribbons are next to each other

Answer 1

Explanation:

Given

there are 12 blue balloon

9 green lanterns

6 red ribbons

Total no of ways in which decoration can be done=(12+9+6)!=27 !

Considering red ribbons as single unit, so there are 22 units

so no of ways in which they are arranged
`=22!* 6!`

6! is multiplied because 6 ribbons can be arranged in 6! ways

No of ways in which decoration is done, such that no two ribbons are next to each other
`=27 !- 22 !* 6!`