At the end of scoring plays in football, a team can score the following totals 2,3,6,7,8. How many five-digits numbers can you make using the digits 2,3,6,7,8? How many of these five-digit numbers are divisible by 6? Explain and justify.

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?