Question

You have 7 balls that are each a different color of the rainbow. In how many distinct ways can these balls be ordered?A. 1B. 7C. 49D. 343E. 5,040

Answer 1

This problem involves permutation since we are dealing with different ways that the colors of the 7 balls can be arranged distinctly. The equation of permutation is described as

`P=(n!)/((n-r)!)`

There are 7 balls in this problem, hence, n = 7. Also, 7 colors are selected at each process of arranging them by color, hence, r = 7. Substitute it on the equation above and compute, we get

`P=(7!)/((7-7)!)`

The expression above can be simplified as

`\begin{gathered} P=(7!)/(0!) \\ P=(1*2*3*4*5*6*7)/(1) \\ P=5040 \end{gathered}`

Answer: E. 5040