How many possible phone numbers can we make out of XXX – XXXX, where X can be any number 0-9? with and without repetition.
Well, the possibilities are endless! With repetition, we have 10 choices for each of the 7 X's, so that gives us a grand total of 10^7 possible phone numbers. Without repetition, we have 10 choices for the first X, 9 choices for the second X (since we can't repeat the number), 8 choices for the third X, and so on. This means we would have 10x9x8x7x6x5x4 = 604,800 possible phone numbers. That's a whole lot of numbers to dial! Just don't forget to save the funny ones in your speed dial, like 1-800-HA-HA-HA.
To calculate the number of possible phone numbers, we need to consider whether repetition is allowed or not.
1. Without repetition:
In this case, each digit of the phone number can only be used once.
The first digit can be any of the 10 numbers (0-9).
The second digit can be any of the 9 remaining numbers (excluding the one already used).
The third digit can be any of the 8 remaining numbers.
The fourth digit can be any of the 7 remaining numbers.
The fifth digit can be any of the 6 remaining numbers.
The sixth digit can be any of the 5 remaining numbers.
Therefore, the total number of possible phone numbers without repetition is:
10 x 9 x 8 x 7 x 6 x 5 = 151,200
2. With repetition:
In this case, each digit can be chosen from the numbers 0-9 including repetition.
For each position, there are 10 possible choices. Since there are 8 positions (XXX-XXXX), the total number of possible phone numbers with repetition is:
10^8 = 100,000,000
So, the number of possible phone numbers without repetition is 151,200, and with repetition is 100,000,000.
To find the number of possible phone numbers, we need to consider the number of options for each digit and whether repetitions are allowed or not.
1. Without repetition:
In this case, once we use a digit, we cannot use it again. For the first digit, we have 10 options (0-9), for the second digit, we have 9 options (excluding the already used digit), and so on. Thus, the number of possible phone numbers without repetition is calculated as:
Number of options for the first digit * Number of options for the second digit * ... * Number of options for the last digit.
So, the total number of possible phone numbers without repetition is: 10*9*8*7*6*5 = 151,200.
2. With repetition:
In this case, we can use the same digit multiple times. For each digit, we still have 10 options (0-9). Therefore, the number of possible phone numbers with repetition is calculated as:
Number of options for each digit^(Number of digits)
So, the total number of possible phone numbers with repetition is: 10^7 = 10,000,000.
Therefore, without repetition, there are 151,200 possible phone numbers, and with repetition, there are 10,000,000 possible phone numbers.
Here is your 7 digit phone number represented with a blank line for each digit.
So the first x can be 10 different numbers _10__ ___ ___ ____ ____ ____ ____, but which ever number you use, it is then used up.
So then you only have 9 numbers left
_10_ x _9_ x ___ x ___ x ___ x ___ x ___
then once that number is used up you have one less number for the next digit of the phone number... and so on
10 x 9 x 8 x 7 x 6 x 5 x 4