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 using the given digits {1,1,2,5,5,5,6,7}, we can break down the problem into smaller steps.
Step 1: Determine the number of digits in the even numbers less than 5,000,000.
Since we are looking for numbers less than 5,000,000, the first digit can be any number from 1 to 4. This gives us 4 possible choices for the first digit.
For the remaining 6 digits, we can use any of the given digits {1,1,2,5,5,5,6,7} without any restrictions. This means we have 8 options for each of the remaining 6 digits. Therefore, the total number of possibilities for the remaining 6 digits is 8^6.
Step 2: Multiply the possibilities from Step 1.
To get the total number of even numbers less than 5,000,000, we need to multiply the number of possibilities for the first digit and the number of possibilities for the remaining 6 digits.
Total number of even numbers = (Number of possibilities for first digit) * (Number of possibilities for remaining 6 digits)
Total number of even numbers = 4 * 8^6
Now we can calculate the answer.
Total number of even numbers = 4 * 8^6
= 4 * 262,144
= 1,048,576
Therefore, there are 1,048,576 even numbers less than 5,000,000 that can be formed using the given digits {1,1,2,5,5,5,6,7}.