Question

You have 7 balls that are each a different color of the rainbow. In how many distinct ways can these balls be ordered?

Answer 1

You have 7 balls that are each a different color of the rainbow. Then, the number of distinct ways in which these balls can be ordered will be given by 7!. 7! = 7*6*5*4*3*2 = 5040 ways. Thus, in 5040 ways, the number of balls can be put in distinct arrangements.

Explanation:

In Short Term 5,040

Answer 2

To solve this question, use a factorial. This is a basic concept in permutations. The first ball can be placed into any of the 7 positions. The second can be placed in 6. The third can be placed in 5, and so on until there are no balls left. One easy way to solve this is to use 7!, or seven factorial. 7! = 7*6*5*4*3*2*1. The answer is 5,040 distinct ways.
Hope that answered your question.