Two two-digit counting numbers (from 10 to 99, inclusive) were chosen randomly.These two integers could be the same or different. What is the probability that thedifference between these two numbers is at most 3?
if the small one is 10 then the other can be 11,12 or 13 That is 3 possibilities
from 11 to 95 inclusive there is 95-11+1=85 numbers each with 3 possible matches
if the small one is 96 then the other can be 97, 98, 99 That is 3 possibilities
if the small one is 97 then the other can be 98,99 That is 2 possibilities
if the small one is 98 then the other can be 99 That is 1 possibilities
So I have 87*3+2+1 = 264 favourable pairs
Now there are 90 numbers to start with. So 90C2= 4005 pairs are in the sample space
so the probability of the desired event happening is 264/4005 = 88/1335
I have not checked for silly errors.