I will give you an illustration:

Suppose there 2 bags. Bag number 1 contains 20 balls, but only one marked with secrete code. The other bag has 7 balls, one also marked with secrete code. I am groping to get one from each bag. What is the chance the I get those marked with secrete codes simultaneously.

From bag #1, I have 1 out 20 chance.

From bag #2, I have 1 out 7 chance.

For both to happen, I will have (1/20)(1/7) = 1/240 chance to hit the jackpot.

If I have 2 bags same as bag #1, 3 bags same as #2, I will have

chance.

You should get it now.