the no. of four digit even numbers that can be formed with 0,1,2,3,7,8

Question

the no. of four digit even numbers that can be formed with 0,1,2,3,7,8

Answer 1

0,1,2,3,7,8 6*5*4*3=360 4-digit numbers 360/2=180 are even and 180 are odd eliminate the ones that start with 0 0_ _ 2 1,3,7, and 8 can go in the other two places 13,17,18,37,38,78 and the reverse of each for a total of 12 0_ _ 8 1,2,3, and 7 can go in the other places 12,13,17,23,27,37 and the reverse of each for a total of 12 180-12-12=180-24=156 4-digit numbers

Answer 2

To be an even number, it would have to end is either 0, 2 or 8.  It does not matter which 3 numbers precede it.

 

_ _ _ _

 

(Any of the remaining 5 numbers) (Any of the remaining 4) (Any of the remaining 3) (Any of the 3 even numbers)

 

However, we must keep in mind that order matters (in other words, 2378 and 2738 are different). So we can use permutations to simplify the above to say:

 

(Any permutation of 3 numbers from the other 5 numbers) * (One of the 3 even numbers)

= (5P3) (3P1)

= (5!/2!) * (3!/2!)

= 60 * 3

= 180