a) There are 167,960 different lists.
b) 60,949,323,800 different lists.
How to find the combinations and permutations?
a) There are 20 students in total, and the list will contain 9 students in no particular order, so we just need to find the combination C(20, 9).
Remember that:
C(N, K) = N!/(N - k)!*K!
Then we will have:
C(20, 9) = 20!/(20 - 9)!*9! = 20!/(11!*9!)
= (20*19*18*17*16*15*14*13*12)/(9*8*7*6*5*4*3*2*1) = 167,960
There are 167,960 different lists.
b) Now we have the same problem, but this time order does matter, so now we count permutations. The number of permutations is given by:
P(N, K) = N!/(N - K)!
Then we will have:
P(20, 9) = 20!/(20 - 9)! = 20*19*18*17*16*15*14*13*12 = 60,949,323,800 different lists.
If you want to learn more about combinations and permutations:
https://brainly.com/question/11732255
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