“Daddy, what are these six colored balls for?”
“Well, son, you’ll notice that three of them are red, two blue and one is green. The red balls all have the number one printed on them, the blue balls all have the number two printed on them, and the green one the number three printed on it,” said daddy, holding up the balls.
“They have very pretty colors, daddy,” said Lenny, “so what do you have in mind.”
“Let’s see how many different six-digit numbers you can make, son,” replied daddy.
“I know already, daddy,” smiled Lenny, “but for the chemistry set you promised me, I’ll tell you how many numbers with digits from one to five can be made with these balls,” said Lenny enthusiastically.
“That’s certainly a deal, son,” said a nonplussed daddy.
How many distinct six figure numbers do you say can be made using these balls?
And, how many distinct numbers with one to five digits can be made with these balls?