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

The is the first concept of permutations.

Let's focus on each ball.
For the first ball, it can be placed into any of the 7 positions.
For the second ball, it can be placed into any of the remaining 6 positions.
For the third ball, you have 5 positions.
For the fourth ball, you have 4 positions.
For the fifth ball, you have 3 positions.
For the sixth ball, you have 2 positions.
For the seventh ball, you have 1 position.

Multiplying it out, the number of ways to arrange 7 distinctly colored balls is:
7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040 ways.

This is used so frequently in combinatorics and probability that it is abbreviated as 7! ("seven factorial").

Answer:
5040 ways

Answer 2

btw welcome to OS :)

Answer 3

thanks