A small lottery was devised using three sets of balls. One ball from each set is drawn. To win the lottery you

have to get the correct number of the sum of the three balls. The sum of the balls cannot be divisible by $7$ or $9.$

The balls are redrawn until the sum is not divisible by $7$ or $9.$ The first set of balls has the numbers $0$ through

$10(0,1,2,3$dots,$10).$ The second set of balls has the even numbers from $0$ to $20(0,2,4,$dots$20),$ and the third set

counts by $3\text{'}$s to $30(0,3,6,$dots,$30).$ Write a program that has as input a number that has been chosen by a lottery

participant $($win$\_$number$).$ The program should return the number of possible winning permutations for

win$\_$number $($winning$\_$permutations$),$ and the total number of possible permuations $($total$\_$permutations$).$

total$\_$permutations should not include permutations that are divisible by $7$ or $9.$

M def win$($win$\_$number$)$:return winning$\_$permutations,total$\_$permutations

M

assert win$(14)==(0,992)$

assert win$(12)==(18,992)$

assert $\}\backslash$operatorname$\{$win$\}(39)==(34,992$

Write a program that calls the function that you have just written, win$(),$ to find the win$\_$number that is most

probable $($best$\_$pick$).$ Please notice that you should return win$\_$number and not the number of winning

permutations of win$\_$number. If you have written win$()$ correctly, there is one win$\_$number that has the greatest

number of possible winning combinations.

Calling win$()$ returns two values. The following cell demonstrates how to call a function with more than one

returned value.

$a,b=$win$(12)$

$pr{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(a)$

$pr{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(b)$

$|$ def max$\_$win$\_$number$()$:return best$\_$pick