Question 316914: how many 5 digited odd numbers be formed using the digits 0,1,2,3,4,5 without repetition
a)120 b)96 c)56 d)72 e)54
Found 2 solutions by solver91311, fcabanski:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
None of your answers is correct either way I do this.
Look at the last digit first. Since the 5 digit number must be odd, the last digit can only be 1, 3, or 5.
Case 1: Assume that the leading digit CANNOT be zero.
Then for each of the 3 ways to choose the last digit, from the originally available 6 digits we subtract 2, namely the digit picked for the last digit and the digit 0, leaving 4 choices, and 3 times 4 equals 12 different ways to select the first and last digits.
For each of those 12 ways to select the first and last digits, there are again 4 ways to select the second digit because the zero has again become available. 48 ways to select the first, second, and last digits.
For each of those 48 ways, there remain 3 unused digits from which we can select the third digit. 3 times 48 is 144.
For each of those 144 ways to select the first, second, third, and last digits, there remain 2 unused digit choices. 2 times 144 is 288.
Recap: 4 times 4 times 3 times 2 times 3 is 288 different 5 digit numbers such that the number is odd and does not begin with zero given the six non-repeatable digits 0, 1, 2, 3, 4, 5.
Case 2: In the improbable event that zero is allowed as a lead digit, then:
5 times 4 times 3 times 2 times 3 is 360 different 5 digit numbers such that the number is odd given the six non-repeatable digits 0, 1, 2, 3, 4, 5.
Either way, the correct answer is not among your choices.
There is a way to make this come out to one of the given answers and that is if you made an error when you listed the available digits. If the available digits were 1, 2, 3, 4, and 5, then you would have 
John
Answer by fcabanski(1391)  (Show Source):
You can put this solution on YOUR website! Cannot be repeated means the same number can't appear twice in a row. It does not mean the same number can't be used in non consecutive digits.
|
|
|
