A shopkeeper sells three varieties of perfumes and he has a large number of bottles of the same size of each variety in his stock. There are 5 places in a row in his showcase. The number of different ways of displaying the three varieties of perfumes in the show case, is

Explanation

Case-I: 3 alike and 2 different does
`""^(3)C_(1)xx""^(2)C_(2)xx(5!)/(2!2!) =60`
Case-II: 2 alike of one kind, 2 alike of another kind and one of third kind.
`""^(3)C_(2)xx""^(1)C_(1)xx(5!)/(2!2!)=90`
`:.` Total ways of arranging =90+60=150