Math CentralQuandaries & Queries


Question from jameka, a student:

How many odd numbers can be written from the set {2,3,4,5,6} if no digits may be used more than once?


One digit numbers are easy, there are only two of them, 3 and 5.

Each of these one digit numbers can be extended to a two digit number by putting a digit in the tens place. Since you can't repeat digits you have four choices of digits to put in the tens place and hence you have 2 × 4 = 8 possible two digit numbers. they are

23, 43, 53, 63, 25, 35, 45, and 65.

Now extend each of these to a three digit number by placing a digit in the hundreds place. How many choices do you have for the digit in the hundreds place? How many three digit numbers are there?

How many four digit numbers? How many five digit numbers?


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