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Answer:

32 4-digit numbers that can be formed using the digits 0,1,2,3,4,5,6,7,8 and 9 without repetition such that the number is divisible by 4 and 5 both.

Step-by-step explanation:

To form a 4-digit number divisible by 4 and 5, the last two digits must be a multiple of 20 (since 5 and 4 have no common factors other than 1). So, the last two digits can be 20, 40, 60, or 80.

For the first two digits, we have 8 choices (since we cannot start with a 0).

So, the total number of 4-digit numbers that can be formed is 8 * 4 = 32.

We can also use permutation and combination to solve this problem.

Step 1: Choose the last two digits

There are 4 ways to choose the last two digits (20, 40, 60, or 80).

Step 2: Choose the first two digits

For the first two digits, we have 8 choices (since we cannot start with a 0).

Step 3: Total number of 4-digit numbers

The total number of 4-digit numbers is the product of the number of ways to choose the last two digits and the number of ways to choose the first two digits. This is 4 * 8 = 32.

Therefore, there are 32 4-digit numbers that can be formed using the digits 0,1,2,3,4,5,6,7,8 and 9 without repetition such that the number is divisible by 4 and 5 both.