How many even numbers of 5 digits without repetition can be formed with the digits 1,2 3 4 and 5?

The correct option is D

312

Even numbers can be formed by placing either 0 or 2 or 4 in the rightmost digit.

_ _ _ _ 0

_ _ _ _ 2

_ _ _ _ 4

So, let us consider all the 3 cases separately.

Case 1: Rightmost digit is 0
Available digits - 1,2,3,4,5

Leftmost digit can be filed with 1 or 2 or 3 or 4 or 5

So, number if ways of filling leftmost digit = 5

As 2 digits are already used, the next position can be filled with either of the 4 digits.

Proceeding in this manner, the next 2 digits can be filled in 3 and 2 ways respectively

|5|4|3_0|2

So, the number of possible numbers = 5×4×3×2 = 120

Case 2: Rightmost digit is 2

_ _ _ _ 2 Available digits 0,1,3,4,5

Out of these 5 digits leftmost digit can be filed with 1 or 3 or 4 or 5
As if 0 comes on the left most position the number will become a 4 digit number.
So, number if ways of filling leftmost digit = 4
As 2 digits are already used, the next position can be filled with either of the 4 digits .

Proceeding in this manner, the next 2 digits can be filled in 3 and 2 ways respectively.

|4|4|3_2|2

So, the number of possible numbers = 4×4×3×2 = 96

Case 3: Rightmost digit is 4
This case is similar to 2nd case.

|4|4|3_4|2

Number of possible numbers = 4×4×3×2 = 96

the total number of arrangements = 120 + 96 + 96 = 312

How many 5 digit even numbers can be formed using the digits 1,2 3 4 5 exactly once?

∴ the total number of arrangements = 120 + 96 + 96 = 312.

How many 5 digit numbers can be formed from the digits 1,2 3 4 5 using the digits without repetition 6 marks I how many of them are even?

Therefore, there will be 60 distinct 5 - digit numbers.

How many 5 digit numbers can make using 5 digits without repeating?

In their numeric form, these numerals have a total of 5 digits. Given: 5- digit numbers starting with 5 without repeating numbers from 0-5. Therefore, possibility of 5 digit numbers are 1 × 4 × 4 × 4 × 4 = 256. Hence, only 256 5-digit numbers can be made starting with 5 without repeating the digits from 0-5.

How many 5 digit numbers are there with no digit being repeated?

Therefore, the number of 5-digit numbers that can be formed by using the digits 0, 1, 2,…..,7 is 5880. Hence, option D is the correct answer.