given the digits {1,1,2,5,5,5,6,7} how many even numbers less than 5 000 000 are there?
To find the number of even numbers less than 5,000,000 that can be made using the given digits {1, 1, 2, 5, 5, 5, 6, 7}, we need to follow these steps:
1. Determine the possible positions for each digit:
- For the first digit (from the left), it can be any of the given digits except for the number 1, as we want the number to be less than 5,000,000.
- For the remaining digits, any of the given digits can be used.
2. Calculate the number of possibilities for each digit position:
- The first digit position (from the left) has 7 possibilities (2, 5, 5, 5, 6, 7).
- The remaining five digits can be any of the given digits (1, 1, 2, 5, 5, 5, 6, 7).
3. Multiply the number of possibilities for each digit position:
- Multiply 7 (for the first digit) by the total number of possibilities for the remaining five digits, which is 8 (as there are eight options).
- Calculate: 7 * 8 = 56
Therefore, there are 56 even numbers less than 5,000,000 that can be made using the given digits {1, 1, 2, 5, 5, 5, 6, 7}.