A shop keeper sells threee 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
A.
6
B.
50
C.
150
D.
None of these
Answer :
150
Solution :
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 $$ = {\,^3}{C_2}\left[ {{2^5} - 2} \right]$$
[$$\because $$ There are two ways when all places will be occupied by single variety each.]
$$\therefore $$ No. of way of displaying all three varieties
$$ = {3^5} - 3 - {\,^3}{C_2}\left( {{2^5} - 2} \right) = 150$$
Releted MCQ Question on Algebra >> Permutation and Combination
Releted Question 1
$$^n{C_{r - 1}} = 36,{\,^n}{C_r} = 84$$ and $$^n{C_{r + 1}} = 126,$$ then $$r$$ is:
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated are
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