Combinatorics question

by **Eddie Gutia** Sun Oct 05, 2014 3:56 pm

The below question is from MGMAT Number properties strategy guide, page no : 48. Below is the question:

An office manager must choose a five-digit lock code for the office door. The first and last digits of the code must be odd, and no repetition of digits is allowed. How many different lock codes are possible?

The answer to this question is 5*8*7*6*4.
But I think the answer should be 5*9*8*7*4, since the integer zero should also be considered. Can you please clarify?

by **tim** Mon Oct 06, 2014 5:54 am

Zero is indeed considered. The reason the 8 is there is because the way to do this one (or any problem of this type) is to work through the restrictions first. There are 5 odds to choose for the first digit, which leaves 4 for the last digit. After that, you have used up two digits and have 8 choices for the second digit (and 7 for the third and 6 for the fourth).

by **Eddie Gutia** Mon Oct 06, 2014 9:49 am

You are right. Sorry for the confusion.

Thanks..

by **RonPurewal** Fri Oct 10, 2014 4:30 am

Glad we could help.

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