Find the probability of the event $B= \{\text{NO two people are born in the same month}\}$. There are 9 people involved by the way. Is it $$ 1/12 \cdot 1/11 \cdot 1/10 \cdot 1/9 \cdot 1/8 \cdot 1/7 \cdot 1/6 \cdot 1/5 \cdot 1/4 \cdot 1/3 \cdot 1/2 \cdot 1/1\,? $$
Because the first person has $1/12$ of it being any month and then the next person only has $1/11$ because 1 month was taken out so they are not on the same month... etc