How many 4 digit number 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?
Plz answer using permutation and combination if possible.
Share
How many 4 digit number 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?
Plz answer using permutation and combination if possible.
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Verified answer
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.