a shopkeeper sells three varieties of perfumes and he has a large number of bottles of the same size of each variety in 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
Answers
Answer: The number of different ways of displaying the three varieties of perfumes in the showcase is 150.
Step-by-step explanation:
There are 5 places in shopkeeper’s show case and has three varieties of perfumes. We can conclude that there would be two cases.
Case 1
Three are of same kind of perfumes and 2 are of different kind of perfumes, so
Number of Arrangements of perfume bottles in his showcase= C(3,1)*C(2,2)*5!/3!
=> 3*1*5*4= 60 (because C(3,1)=3 & C(2,2)=1)
Case 2
Two pairs of perfumes are of same kind and one is different, so
Number of Arrangements of perfume bottles in his showcase= C(3,2)*C(1,1)*5!/(2!*2!)
=> 3*1*5*4*3/2= 90 ( because C(3,2)=3 & C(1,1)=1)
Therefore,
Total number of arrangements of perfume bottles in his showcase= 60+90=150