Question

There are 5 different caps $c_1,c_2,c_3,c_{4}and{c}_5$ and 5 different boxes $B_1,B_2,B_3,B_{4}and{B}_5$. The capacity of each box is sufficient to accomodate all the 5 caps.

If all the caps are of different colours and each box can have only one cap, in how many ways can you arrange the caps among the 5 boxes?

• A. 120
• B. 180
• C. 360
• D. none of these

Answer 1

The correct option is A 120

Required number of arrangements ${=}^5{P}_5$
${}^5{P}_5=5\times 4\times 3\times 2\times 1=120$