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!!!Please somebody can explain me this!!!
how many even digits are there from 0 - 9 ??
there are 5
how many digits are there from 0 to 9 ?
there are 10
so you have 5 choices as the first digit, 5 choices again for the second digit, 10 choices for the 3rd digit, etc
Thanks, but what about the odd number?
let's see. You know there are 10 digits
You know there are 5 even digits.
asking now how many odd digits there are is the same as holding out both hands, and when someone says, "This one is your left hand," you ask, well, which one is my right hand?
In the old system, a security code consisted of two odd digits, followed by four even digits. Since there are 10 different digits (0-9), the number of possibilities for each odd digit is 5 (1, 3, 5, 7, or 9), and the number of possibilities for each even digit is also 5 (0, 2, 4, 6, or 8).
Therefore, for the old code, there are 5 options for the first odd digit, 5 options for the second odd digit, 5 options for the first even digit, 5 options for the second even digit, 5 options for the third even digit, and 5 options for the fourth even digit. Multiplying all of these options together, we get: 5 x 5 x 5 x 5 x 5 x 5 = 15,325 possible codes.
In the new system, a security code consists of two even digits, followed by any three digits. Since we now have two even digits to choose from, there are 5 options for the first even digit and 5 options for the second even digit.
After selecting the two even digits, we can choose any of the 10 digits (0-9) for each of the three remaining digits. Therefore, there are 10 options for each of the three remaining digits.
Multiplying all of these options together, we get: 5 x 5 x 10 x 10 x 10 = 25,000 possible codes in the new system.
To find the increase in the number of possible codes, we subtract the number of possible codes in the old system from the number of possible codes in the new system, getting: 25,000 - 15,325 = 9,675.
Therefore, the increase in the number of possible codes is 9,675.