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Using the digits [tex]$1, 4, 6,$[/tex] and [tex]$8$[/tex] each only once, how many four-digit odd numbers can be formed?

A. 4
B. 5
C. 3
D. 6


Sagot :

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
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