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  • How many different two-digit numbers can be formed using the digits 0, 1, 2, and 3 by swapping the positions of two digits?  <s

How many different two-digit numbers can be formed using the digits 0, 1, 2, and 3 by swapping the positions of two digits?

 

Option: 1

10


Option: 2

12


Option: 3

9


Option: 4

6


Answers (1)

best_answer

To find the number of different two-digit numbers that can be formed using the digits 0,1,2, and 3 by swapping the positions of two digits, we need to consider the different arrangements that result from swapping the positions of two digits.

Since the first digit cannot be zero, there are a total of 3 choices for the first digit (1,2, or 3). After choosing the first digit, there are 3 remaining digits to choose from for the second digit.

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 tens and ones digits of 21 and swapping the ones and tens digits of 12 both result in the number 12.

Therefore, the number of different two-digit numbers that can be formed by swapping the positions of two digits from the digits

\mathrm{0,1,2, \, \, and\, \, 3 \, \, is \, \, (3 \times 3) / 2=9.}

Posted by

HARSH KANKARIA

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