A four digit even number is formed by using the digits 0, 1,2,3,4,5 without repetition of digits Find the - Maths - Probability

Question

A four digit even number is formed by using the digits 0, 1,2,3,4,5
without repetition of digits Find the probability that the number
is divisible by 5 ?

Akhil Goyal · Accepted Answer

Since the number is even, the number must have 0 in the end to be divisible by both 5 and 2
So, we need to place any 3 digits from the set {1,2,3,4,5} on rest three places
Possible ways of doing this = C35×3!=60Now we need to calculate total ways of forming a 4 digit even number from the set {0,1,2,3,4,5}:Units place can only take {0,2,4}
 If there's 0 in the units place then, total posibilities are = C35×3!However, if there's 2 in the end then (we need to subract the cases when there's 0 in the ten thousandth place) total possiblities are=C35×3! - C24×2!Same goes for when there's 4 in the end
So total possibilities are = C35×3!+2C35×3! - C24×2!=60+2(60-12)=156Therefore final answer = 60156=513

A four digit even number is formed by using the digits 0, 1,2,3,4,5 without repetition of digits. Find the probability that the number is divisible by 5 ?