Bunuel wrote:

What are the odds that a 3-digit number contains 3 distinct prime numbers?

A. 3/125

B. 2/75

C. 24/899

D. 3/50

E. 1/15

One-digit distinct prime numbers are {2,3,5,7}.

From 999 to 100 their are \(999-100+1=900\) different 3-digit numbers.

Favorable outcomes starting from 200 is: {235,237,253,257,273,257} = 6, and the same result will also be for, 300, 500 and 700.

So, the favorable outcomes for all 3-digit number containing 3 distinct prime numbers is \(6*4=24\).

Thus, odds are: \(\frac{Favorable.Outcomes}{Total.Outcomes}=\frac{24}{900}=8/300=4/150=2/75\)

(B) is the answer.