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  • If the digits 1, 2, 3, 4, and 5 are arranged to form a five-digit number, how many different numbers can be created by swapping the positions of any two digits?  <div class='qna-

If the digits 1, 2, 3, 4, and 5 are arranged to form a five-digit number, how many different numbers can be created by swapping the positions of any two digits?

 

Option: 1

16


Option: 2

22


Option: 3

10


Option: 4

40


Answers (1)

best_answer

To find the number of different five-digit numbers that can be created by swapping the positions of any two digits from the digits 1,2,3,4, and 5, we need to consider the different arrangements that result from swapping the positions of any two digits.

Since there are five digits, there are a total of 5 choices for the first digit. After choosing the first digit, there are 4 remaining digits to choose from for the second digit. Therefore, there are 5^* 4=20 possible arrangements so far.

However, we need to divide this total count by 2 to account for the fact that swapping the positions of two digits can result in the same number. For example, swapping the thousands and ones digits of 12345 and swapping the ones and thousands digits of 21345 both result in the number 21345.

Therefore, the number of different five-digit numbers that can be created by swapping the positions of any two digits from the digits 1,2,3,4, and 5 is (5 \times 4) / 2=10

Posted by

Ritika Kankaria

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