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  • How many distinct three-digit numbers can be formed using the digits 5, 6, 7, and 8 by swapping the positions of two digits?  <

How many distinct three-digit numbers can be formed using the digits 5, 6, 7, and 8 by swapping the positions of two digits?

 

Option: 1

15


Option: 2

14


Option: 3

10


Option: 4

18


Answers (1)

best_answer

To find the number of distinct three-digit numbers that can be formed using the digits 5,6,7, and 8 by swapping the positions of two digits, we need to consider the different arrangements that result from swapping the positions of two digits.

There are three possible positions to swap: the tens digit, the hundreds digit, and the ones digit.

For each position, we can swap one of the four digits with one of the remaining three digits. This gives us a total of 3 \times 4 \times 3=36 distinct arrangements.

However, we need to divide this number by 2 to account for the fact that swapping the positions of two digits can result in the same number. For example, swapping the tens and ones digits of 567 and swapping the ones and tens digits of 576 both result in the number 567.

Therefore, the number of distinct three-digit numbers that can be formed by swapping the positions of two digits from the digits 5, 6, 7, and 8 is 36 / 2=18.

Posted by

Suraj Bhandari

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