Final answer:
There are 780 different numbers not exceeding 10000 that can be made using the digits 2,4,5,6,8 if repetition of digits is allowed. Calculations are based on combinations for 1 to 4-digit long numbers.
Step-by-step explanation:
To find how many numbers not exceeding 10000 can be made using the digits 2,4,5,6,8 with repetition allowed, we have to consider numbers of different lengths (1 to 4 digits) separately.
For a 1-digit number, there are 5 choices (2, 4, 5, 6, or 8).
For a 2-digit number, there are 5 choices for the first digit and 5 choices for the second digit, making a total of 5 x 5 = 25 combinations.
For a 3-digit number, there are 5 choices for the first digit, 5 choices for the second digit, and 5 choices for the third digit resulting in 5 x 5 x 5 = 125 combinations.
For a 4-digit number, there are 5 choices for each of the four digits so, 5 x 5 x 5 x 5 = 625 combinations.
Add up all the possibilities for 1-digit, 2-digit, 3-digit, and 4-digit numbers: 5 + 25 + 125 + 625 = 780.
Therefore, there are 780 different numbers that can be created using the digits 2,4,5,6,8 without exceeding 10000.
Therefore answer is c. 780.