Permutations And Combinations Question 354

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

Options:

A) 6

B) 50

C) 150

D) None of these

Show Answer

Answer:

Correct Answer: C

Solution:

  • [c] Number of ways of displaying without restriction $ =3^{5} $ Number of ways in which all places are occupied by single variety $ =3\times 1 $ Number of ways in which all places are occupied by two different varieties $ {{=}^{3}}C_2[2^{5}-2] $ [ $ \because $ There are two ways when all places will be occupied by single variety each.]
    $ \therefore $ No. of way of displaying all three varieties $ =3^{5}-3{{-}^{3}}C_2(2^{5}-2)=150 $