Final answer:
To find the number of numbers divisible by 5 and lying between 40000 and 50000 that can be formed from the digits 0, 3, 4, 5, 8, and 9 with repetition of digits allowed, we can use permutations. The answer is 600.
Step-by-step explanation:
To find the number of numbers divisible by 5 and lying between 40000 and 50000 that can be formed from the digits 0, 3, 4, 5, 8, and 9 with repetition of digits allowed, we can use the concept of permutations.
Step 1: Create a number from the given digits that is divisible by 5. The digit 0 cannot be the first digit, so we have 5 choices for the first digit. The remaining digits can be arranged in any order, so we have 5! = 120 arrangements for the remaining digits.
Step 2: Determine the number of digits that can be repeated. The only digit that can be repeated is 0, so we have 1 option for repetition.
Step 3: Multiply the number of choices for each step: 5 x 120 x 1 = 600.
There are 600 numbers divisible by 5 and lying between 40000 and 50000 that can be formed from the given digits with repetition allowed. Therefore, the answer is 600.