Question

How many even numbers lying between 200 and 500 can be formed from the figures 1, 2, 3, 4, 5 and 6 if no figure is to appear more than once in any number.

Answer 1

Each even number is to lie between 200 and 500.

Hence, the position on the left in x x x is to be filled with 2, 3 or 4. When 2 or 4 is filled on the left, the position on the right can be filled with the remaining 2 even figures in 2 ways and the middle position can be filled with the remaining 4 figures in 4 ways. 

Therefore, the total number of ways of forming the even numbers in this case = 2 . 4 . 2 = 16.

When 3 is filled on the left, the position on the right can be filled with the 3 even figures in 3 ways, and the middle position can be filled with the remaining 4 figures in 4 ways. Therefore, the total number of ways of forming the even numbers in this case = 1 . 4 . 3 = 12.

Therefore, the required number = 16 + 12 = 28.