Sorry for so many questions today guys. But this set will be last set for this week.

Have some probability problems I'm doing in discrete math. I have done most of them but have trouble on starting for some of them and want to check answers on some as well.

Here I go:

Ok for problem 8:

there are 36 possible outcomes

e isn't a trick question is it? it's basically the same as a thru d correct?

i think i have this question done correctly

Problem 9: should be number of multiples of 7 plus multiples of 3 for 5 digits minus number of multiples for 21. so i think i have this done correctly

Problem 10 is what I'm having trouble with. Seems like there are many ways total and I was going to use the probability tree but it doesn't work as well as it would on problem 11.

Problem 11: used tree, got 88888 different pins.

Haven't started 13..but should be similar to 12...no?

14. I used a formula. P(n,r) = n(n-1)(n-2)...(n-r+1)

i set the equation as P(n,5) = (n-5+1) then n-6=2027400

got n as 2027406 and used that for (2027406)!/(5!*2027401!)

Any input would greatly be appreciated, thanks for you help again!