Question

The number of 4 digit even numbers that can be formed using 0, 1, 2, 3, 4, 5, 6 without repetition is
A. 120
B. 300
C. 420
D. 20

Answer 1

Now the hint for this problem can simply be which numbers we call are even and what does without repetition mean? That’s it! So even numbers having the unit's place digit are either 0, 2, 4, 6. Thus we can put these numbers in the unit's place. But once they are placed in this they can't be repeated. So let’s solve it.

Complete step by step answer:
We have 7 digits in total 0, 1, 2, 3, 4, 5, 6
Now among that 0, 2, 4, 6 are even.
Now we need to form a four digit number so we cannot place 0 to the leftmost place.
So the choices are only 6.
But it can definitely be placed on the rightmost place.
Thus we have if 0 in unit’s place then the possible number will be, $6 \times 5 \times 4 \times 1 = 120$
Because 0 is fixed on the unit's place thus only 1 choice. Remaining digits can be placed from the leftmost place with 1 down each next place.
Now if unit’s place digits are either 2, 4 or 6
Then the repetition is not allowed so the numbers so formed will be $5 \times 5 \times 4 \times 3 = 300$
Thus total numbers so formed are $300 + 120 = 420$

So, the correct answer is “Option C”.

Note: Note that we might get confused in the case where 2, 4 or 6 can be placed. The choice of second place from left should be decreased by 1 but we should note that 0 cannot be placed on the leftmost place but it can be placed on other places in the number. So the choices are 5 and 5 for both the places.