1. A reconnaissance class has 12 soldiers, including 3 telegraph operators. Now, these 12 soldiers are to be randomly divided into 3 groups, with 3 soldiers, 4 soldiers, and 5 soldiers respectively. The probability that each group has 1 telegraph operator is $\qquad$ .
The number of ways to randomly divide 12 soldiers into 3 groups is $M=C_{12}^{3} C_{9}^{4} C_{5}^{5}$, the number of ways where each group has 1 telegraphist is $m=C_{9}^{2} C_{7}^{3} C_{4}^{4} A_{3}^{3}$, let the required event be $A$, then $P(A)=\frac{m}{M}=\frac{C_{9}^{2} C_{7}^{3} C_{4}^{4} A_{3}^{3}}{C_{12}^{3} C_{9}^{4} C_{5}^{5}}=\frac{36 \cdot 35 \cdot 6}{220 \cdot 126}=\frac{3}{11}$.