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

That would be 7!
= 7*6*5*4*3*2*1 =  5040 ways

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.