Answer :
To determine how many four-digit odd numbers can be formed using the digits 1, 4, 6, and 8, each used exactly once, we will follow these steps:
1. Identify the condition for the last digit: The number must be odd. The only odd digit available in the given set is 1. Therefore, 1 must be the last digit.
2. Arrange the remaining digits: To form the four-digit number, we must arrange the remaining three digits (4, 6, and 8) in the first three positions.
3. Calculate the permutations of the remaining digits:
- The number of ways to arrange three distinct digits, 4, 6, and 8, is given by the number of permutations of these digits.
- The formula for the number of permutations of three distinct objects is \(3!\) (3 factorial), which is calculated as follows:
[tex]\[ 3! = 3 \times 2 \times 1 = 6 \][/tex]
4. Count the valid numbers: Each of these permutations of the first three digits combined with the last digit being 1 will form a unique four-digit odd number.
By this process, we find that there are 6 distinct four-digit odd numbers that can be formed.
Hence, the correct answer is:
(D) 6
1. Identify the condition for the last digit: The number must be odd. The only odd digit available in the given set is 1. Therefore, 1 must be the last digit.
2. Arrange the remaining digits: To form the four-digit number, we must arrange the remaining three digits (4, 6, and 8) in the first three positions.
3. Calculate the permutations of the remaining digits:
- The number of ways to arrange three distinct digits, 4, 6, and 8, is given by the number of permutations of these digits.
- The formula for the number of permutations of three distinct objects is \(3!\) (3 factorial), which is calculated as follows:
[tex]\[ 3! = 3 \times 2 \times 1 = 6 \][/tex]
4. Count the valid numbers: Each of these permutations of the first three digits combined with the last digit being 1 will form a unique four-digit odd number.
By this process, we find that there are 6 distinct four-digit odd numbers that can be formed.
Hence, the correct answer is:
(D) 6
