Question 579978
Inclusion-exclusion principle. (let n be a number between 1 and 600 inclusive):


*[tex \LARGE P(6|n \hspace{2 mm} or \hspace{2 mm} 9|n) = P(6|n) + P(9|n) - P(18|n)]


Note that P(6|n and 9|n) is equivalent to saying P(18|n) since LCM(6,9) = 18.


Out of the integers between 1 and 600 inclusive, there are 100 integers divisible by 6, 66 divisible by 9, and 33 divisible by 18. Therefore,


*[tex \LARGE P(6|n \hspace{2mm} or \hspace{2 mm} 9|n) = \frac{100}{600} + \frac{66}{600} - \frac{33}{100}]


*[tex \LARGE = \frac{133}{600}]