Quandaries
and Queries 

Hello, I'm a parent trying to help my 10 year old and I'm getting confused. The question is: I have four playing cards 2,3,4,5 of hearts. How many three digit numbers can I make from the four cards. I've ended up with 96 three digit numbers and I'm sure that's not right. Help! Is there some kind of formula? Many thanks, Sue 

Hi Sue, Think about actually using the cards to produce a three digit number. You have four cards in front of you so you have 4 choices for the first digit. Regardless of which card you chose for the first digit you have three cards remaining, and you can uses any one of them for the second digit. That is you have 3 choices for the second digit. Thus you have 4 3 = 12 possible two digit numbers. You can actually list them. If you chose 2 as the first digit then the possible two digit numbers are
If you chose 3 as the first digit then the possible two digit numbers are
If you chose 4 as the first digit then the possible two digit numbers are
If you chose 5 as the first digit then the possible two digit numbers are
Now again, regardless of which of the twelve possible two digit number you have formed there are two cards left and hence two ways to complete the three digit number. Hence the number of possible three digit numbers is 4 3 2 = 24. Penny 

