Question

A six digit number is formed by the digits 1, 2, 3, 4, 5, 6 without repetition. what is the probability that the number formed is divisible by 4?

Answer 1

The total no. of 6 digit numbers possible without repetition is,

6*5*4*3*2*1 = 720 number [ I used permutations ] ,

Because Possible values for first place = 6, Possible values fore second place = 5, and so on ,

Now ,

A number is only divisible by 4 if the last 2 digits are divisible by 4,

Let's check out possible combinations of 2 digit number which are divisible by 4,
16, 24, 36, 52, Etc, are the last two digits possible,

Now using permutations again, We can find out how many such numbers are possible,

If last two digits are fixed, then there are 4 numbers remaining so Total number of possible values for 1 fixing is 4*3*2*1 = 24,

There are 4 such Fixing values so,

4*24 = 96,

So there are 96, 6 digit numbers which are divisible by 4, Without repetition,

Now,

Probability = No. of Favourable Out comes / Total no. of Outcomes,

Here No. of Favourable out comes = 96, and Total no . of Outcomes = 720,

Now probability = (4*4*3*2*1)/6*5*4*3*2*1)
=> 4/6*5
=> 4/30
=> 2/15,

Therefore the probability that a number is divisible by 4 in a six digit number is 2/15,

Hope you understand, Have a great day !