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  • The total number of distinct four-digit even numbers if the digit used is not repeated is  Option: 1 1782 <p dir="ltr

The total number of distinct four-digit even numbers if the digit used is not repeated is

 

Option: 1

1782

 

 


Option: 2

2220

 

 


Option: 3

1792

 


Option: 4

 2240


Answers (1)

best_answer

Let the number be ABCD, where A, B, C, and D are the digits.

The digit D can take 4 values. (2,4,6,8).

The digit 'A' can take any digit from 1 to 9 (it cannot take zero because the number would no longer be four digits). However, A cannot have the same value as D. As a result, there are eight possible values for the digit 'A'.

B can also be zero. It must not, however, be the same as A or D. As a result, the digit 'B' can have up to eight possible values.

Similarly, the digit 'C' can have up to seven different values.

Hence, the number of four-digit even numbers is given by,

\mathrm{n=8\times 8\times 7\times 4}

\mathrm{n=1792}

Therefore, the total number of four-digit even numbers is 1792 ways.

 

Posted by

Ritika Kankaria

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