Question 770548: A security code used to consist of two odd digits, followed by four even digits. To allow more codes to be generated, a new system uses two even digits, followed by any three digits. If repeated digits are allowed, the increase in the number of possible codes is____
Answer: Old code: 5x5x5x5x5x5=15325
New code: 5x5x10x10x10=25000
The increase in the number of codes is 9375.
I don't understand why they use 5's and 10's!!!
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
There are 10 possible digits, 0 through 9, for each place in the code. But if a particular place must be either even or odd, then there are only 5 choices for that place -- because of the 10 possible digits, 5 of them are even and 5 of them are odd.
In the case of the old code, there are 5 ways to choose the first digit: it can either be 1, 3, 5, 7, or 9. Then, for each of those choices, there are 5 ways to pick the second digit because you are allowed to repeat digits, namely 1, 3, 5, 7, and 9 again. So just considering the first two positions, there are 5 times 5, which is to say 25 ways to fill them. Then, the next position has 5 ways to fill it...0, 2, 4, 6, 8. And so on.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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