John is choosing a number n randomly from all integers from 56 to 150

Total number of Integers from 56 to 150 inclusive = 150 - 56 +1 = 95

n(n+1) will be divisible by 5 if either 'n' or 'n+1' is divisible by 5. i.e., n should be multiple of 5 or 4.

We need to find how many numbers from 56 to 150 (inclusive) are multiple of 4, multiple of 5, multiple of both.

Total numbers divisible by 4 = (last multiple in the list/4) - (first multiple in the list/4) + 1 = 148/4 - 56/4 + 1 = 37-14+1 = 24

Similarly, Total numbers divisible by 5 = (last multiple in the list/5) - (first multiple in the list/5) + 1 = 150/5 - 60/5 + 1 = 30-12+1 = 19

So, in the list of integers from 56 to 150, we have 24 numbers divisible by 4 and 19 numbers divisible by 5.

However, we also have numbers that are divisible by both 4 and 5 and they need to be subtracted from the total.
i.e. Total Numbers that are divisible by 20 = 140/20 - 60/20 + 1 = 7-3+1 = 5

Hence, total numbers divisible by 4 or 5 = 24 + 19 - 5 = 38

Probability that the chosen number he will be one where n(n + 1) is divisible by 5 = 38 / 95 = 2/5

Answer: C