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  • Kavita has six different colored pairs of earrings (two each of red, blue, and black). He wants to display all of these pairs of earrings. How many different earring arrangements are ther

Kavita has six different colored pairs of earrings (two each of red, blue, and black). He wants to display all of these pairs of earrings. How many different earring arrangements are there?

 

Option: 1

100


Option: 2

60


Option: 3

120


Option: 4

90


Answers (1)

best_answer

The total number of pairs of earrings is n = 6

The number of red earrings is p = 2

The number of blue earrings is q = 2

The number of back earrings is r = 2

Substituting the values in the permutation formula to get,

\mathrm{\begin{aligned} & P R_n^{p, q, r}=\frac{n !}{p ! q ! r !} \\ & P R_6^{2,2,2}=\frac{6 !}{2 ! 2 ! 2 !} \\ & P R_6^{2,2,2}=\frac{720}{8} \\ & P R_6^{2,2,2}=90 \end{aligned}}

Therefore, the earrings can be arranged on the shelf in 90 ways.

Posted by

seema garhwal

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