SEARCH HOME
Math CentralQuandaries & Queries

search

Question from Natalie:

Using The Numbers 7 4 5

How many different 4-digit combinations are possible, you can use any of the numbers twice.

Hi Natalie,

I assume that by "you can use any of the numbers twice" you mean not 3 of 4 times. I also assume that order is important, that is 7475 and 7745 are different.

How many different 4-digit combinations are possible if you can use each of the 4 digits, 7, 4 and 5, as many times as you want? In this case there are 3 choices for each of the 4 digits so the answer is 3 × 3 × 3 × 3 = 81.

How many of these use one of the digits 3 or 4 times? These have to be removed from the 81 you have. Concentrate on 7 for the moment. How many have either 3 or 4 sevens? There is only one containing 4 sevens, 7777. There are four that contain 3 sevens and a four, 4777, 7477, 7747 and 7774.

Can you complete the problem now?
Penny

About Math Central
 

 


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS