Explain and prove your answer for each question. (a) How many lists of length 3 can be formed whose components are drawn from {1, 2, 3, . . . , n}? (b) How many lists of length 3 can be formed whose components are drawn from {1, 2, 3, . . . , n} and if we require that the first and second components must be the same? (c) How many lists of length 3 can be formed whose components are drawn from {1, 2, 3, . . . , n} and the components are all distinct? (d) How many lists of length 3 can be formed whose components are drawn from {1, 2, 3, . . . , n} and if we only require that the first and last components must be different?

a) We have n³ possible lists

b) We have n² possible lists

c) We have n³-3n²+2n possible lists

Step-by-step explanation:

a) We have n options for each element of the list. Since we have no restrictions between the elements, then we will have to power n by 3, gibing us a total of n³ possible lists that we can form.

b) Since the fisrt two components must be the same, then we have n possibilities for the first element and after choosing it, we will have only 1 possibility for the second element and then n possibilities for the third one. This gives us n*1*n = n² possible lists.

c) We have n possibilities for the first element, but we have to discard it when we pick the second one, thus we have n-1 possibilities for the second element and with a similar argument we will have n-2 possibilities for the third element. Giving us a total of n*(n-1)*(n-2) = n³-3n²+2n possibilities.

step-by-step explanation:

your answer is a

the option best identifies the textual evidence that supports this conclusion is c.) when an argument is over, how many weighty reasons does a man recollect which his heat and violence made him utterly forget? in order to recognize textual evidence is to identify the topic sentence where the author states the main idea. textual evidence is what supports the topic sentence or main idea of a passage.