Question

find the probability that a five digit number formed by 1,2,3,4,5 ( not repeated) are divisible by 4?

Answer 1

Given digits are: 1,2,3,4,5.
No. of 5 digit no. that can be formed without repetition is 5! i.e., 120.
Now,
A no. is divisible by 4 only when its last two digits are divisible by 4
But we have only 5 numbers from 1-5, the units place must contain a no. which is a multiple of 4.
So, in this case the units place can be filled only in 1 way, with the no. 4 itself.
The remaining 4 places can be filled with the remaining 4 no.s in 4! ways,i.e. in 24 ways.
Thus,
The required probability= 24/120=1/5.


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