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  • The number of 8-digit numbers that can be formed from the digits 1,2,3,4,5,6,7,8,9  so that digits do not repeat and the terminal digits are even is &nb

The number of 8-digit numbers that can be formed from the digits 1,2,3,4,5,6,7,8,9

 so that digits do not repeat and the terminal digits are even is

 

Option: 1

80640

 


Option: 2

31480


Option: 3

60480

 


Option: 4

42340


Answers (1)

best_answer

The first and last digits are referred to as terminal digits. Here, it is given that the terminal digits are even.

As a result, there are several ways to fill the first position in 4 ways(2, 4, 6, 8).

Since repetition is not allowed and the terminal digits must all be even, we used one even digit at the first position, leaving us with "even" digits. As a result, the final position can be filled in "3 ways."

Now, we have left with '7' digits and '6' places. As we know that these 6 places can be filled with any number even or odd. But the digits cannot be repeated.

Thus, the possible digits for second place will be 7.

The possible digits for third place will be 6.

The possible digits for fourth place will be 5.

The possible digits for fifth place will be 4.

The possible digits for sixth place will be 3.

The possible digits for seventh place will be 2.

So, the total number of numbers that can be formed with the given digits is given by,

4 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 3 =60480

Therefore, the possible number is 60480.

Posted by

jitender.kumar

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