Question

How many even numbers less than 10000 can be formed with the digits 3,5,7,8,9 without any repitition?

Answer 1

38,58,78,98,358,378,398,538,578,598,738,758,798,938,958,978,3578,3597,3758,3798,3958,3978,5378,5398,5738,5798,5938,5978,7358,7398,7538,7598,7938,7958,9358,9378,9538,9578,9738,9758 are the numbers that can be formed

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Answer 2

The required number is less than 10000
this means that it should be of either 4 digits or 3 digits or 2 digits or 1 digit.
And according to condition given in question, these number should end with 8 because it's only even number given there.

Case 1: 4 digit case
let's consider 3 empty places with last place 8 i.e
_ _ _ 8
in order to fill them using digits given in question. Start from right to left,
there are 4C1 ways to fill second last place,
and 3C1 for third last and 2C1 for fourth last,
by multiplication law, we have total places
we have 4C1×3C1×2C1=24

Case 2: 3 digit case
here, we take case similar from case 1 but for 2 empty place and right most place with 8.
clearly just like case one, we will have,
4C1×3C1=12

Case 3: 2 digit case
here right most has 8 and one place is left that can be filled in 4 different ways
=> 4C1=4

Case 4: 1 digit case,
we can only put 8 as even i.e only 1 case

now from addition law, we take the union of all 4 cases i.e 24+12+4+1 = 41 (Ans.)