given the digits {1,1,2,5,5,5,6,7} how many even numbers less than 5 000 000 are there?
If you have to use all 8 digits, there are none less than 5 million.The smallest possible number is then 11,255,567.
If you do not have to use all digits, they should say so.
I have seen this question several times in the last few days.
I agree with drwls that it is too ambiguous.
If anything goes, then this is a monster question, since there are so many cases to consider.
e.g. for a 5 digit number...
1. all digits are different
2. a pair of 1's and the rest different
3. a pair 5's and the rest different
4. a triple of 5's and the rest different
5 a pair of 1's and a pair of 5's, and some other
6. a pair of 1's and a triple of 5's
As you get into 6 and 7 digit numbers you have the same problem
This is why I have ignored the question.
To determine how many even numbers less than 5,000,000 can be formed using the given digits {1, 1, 2, 5, 5, 5, 6, 7}, we need to consider the rules of forming numbers:
1. Rule for the first digit:
- For the first digit, we have five options: {1, 2, 5, 6, 7}.
- The digit cannot be 5 because we want numbers less than 5,000,000.
2. Rule for the remaining digits:
- For the second digit, we have eight options: {1, 1, 2, 5, 5, 5, 6, 7}.
- For the third digit, we have seven options: {1, 1, 2, 5, 5, 6, 7}.
- For the fourth digit, we have six options: {1, 1, 2, 5, 6, 7}.
- For the fifth digit, we have five options: {1, 1, 2, 6, 7}.
- For the sixth digit, we have four options: {1, 1, 2, 7}.
Now, we can multiply the number of options for each digit to find the total number of possibilities:
5 × 8 × 7 × 6 × 5 × 4 = 33600
So, there are 33,600 even numbers less than 5,000,000 that can be formed using the given digits {1, 1, 2, 5, 5, 5, 6, 7}.