There are two decks of 10 cards each. The cards in each deck are labeled with integers from 10 to 20 inclusive. If we pick a card from each deck at random, what is the probability that the product of the numbers on the picked cards is a multiple of 6?	Choose the correct choice from the following answers
A) 0.23 B) 0.36 C) 0.4 D) 0.42 E) 0.46
If 6 is a multiple, we need 2 and 3 as a factor of the number. If we factor the numbers 11 through 20 we have:   11 = 11   12 = 2*2*3   13 = 13   14 = 7*2   15 = 5*3   16 = 2*2*2   17 = 17   18 = 3*2*3   19 = 19   20 = 5*2*2   0.4ombos that have a 2 and a 3 as factors (first + second card):   12 + anything - 19 of these possibilities (we count 12 + 12 only once)   14 + 15 - 2 of these possibilities   15 + 16 - 2 of these possibilities   15 + 20 - 2 of these possibilities   18 + anything (except 12, since that is counted in our first option) - 17 of these possibilities   Total possibilities that will be a multiple of 6: 42   Total possibilites:   10*10= 
<gadget id="calculator">  10*10</gadget>
<output>100</output>
100   Probability= 42/100 = 0.40   Answer:0.4
<result>C</result>
There are two decks of 10 cards each. The cards in each deck are labeled with integers from 10 to 20 inclusive. If we pick a card from each deck at random, what is the probability that the product of the numbers on the picked cards is a multiple of 6?