Section A1: List the elements of the set in roster notation. (Enter EMPTY or ∅ for the empty set.) {x | x is a letter of the word TALLAHASSEE}2: Let A and B be subsets of a universal set U and suppose n(U) = 400, n(A) = 125, n(B) = 90, and n(A ∩ B) = 40. Find the number of elements in the set. n(Ac)3: Let A and B be subsets of a universal set U and suppose n(U) = 400, n(A) = 125, n(B) = 80, and n(A ∩ B) = 60. Find the number of elements in the set n(Ac ∩ B4: Let A and B be subsets of a universal set U and suppose n(U) = 350, n(A) = 115, n(B) = 70, and n(A ∩ B) = 60. Find the number of elements in the set. n(Ac ∩ Bc)BONUS AEvaluate the quantity. 3 · P(5, 2) · C(9, 3) Section B1: The Department of Foreign Languages of a liberal arts college conducted a survey of its recent graduates to determine the foreign language courses they had taken while undergraduates at the college. Of the 500 graduates205had at least one year of Spanish.170had at least one year of French.141had at least one year of German.37had at least one year of Spanish and French.29had at least one year of Spanish and German.22had at least one year of French and German.4had at least one year of all three languages.(a) How many of the graduates had at least 1 yr of at least one of the three languages?(b) How many of the graduates had at least 1 yr of exactly one of the three languages?(c) How many of the graduates had less than 1 yr of any of the three languages? 2: In how many ways can 9 different compact discs be arranged on a shelf?(a) In how many ways can four pictures be selected from a group of ten different pictures? 3: How many three-digit numbers can be formed from the numerals in the set {1, 2, 3, 4, 5} if the following is true?(a) Repetition of digits is not allowed(b) Repetition of digits is allowed4: Five soups, two entrées, and four desserts are listed on the "Special" menu at the Neptune Restaurant. How many different selections consisting of one soup, one entrée, and one dessert can a customer choose from this menu?BONUS BIn a survey conducted by Helena, a financial consultant, it was revealed of her 420 clients279 own stocks.192 own bonds.182 own mutual funds.115 own both stocks and bonds.98 own both stocks and mutual funds.96 own both bonds and mutual funds.How many of Helena's clients own stocks, bonds, and mutual funds? (Assume each client invested in at least one of the three types of funds.) Section C 1: In an election being held by the Associated Students Organization, there are eight candidates for president, three for vice-president, five for secretary, and six for treasurer. How many different possible outcomes are there for this election?2: There are eight seniors and five juniors in the Math Club at Jefferson High School. In how many ways can a math team consisting of four seniors and three juniors be selected from members of the Math Club? 3: From a shipment of 60 transistors, 3 of which are defective, a sample of 5 transistors is selected at random.(a) In how many different ways can the sample be selected?(b) How many samples contain exactly 3 defective transistors?(c) How many samples do not contain any defective transistors? BONUS CA sample of 4 balls is to be selected at random from an urn containing 16 balls numbered 1 to 16. Six balls are green, 5 balls are white, and 5 balls are black.(a) How many different samples can be selected?(b) How many samples can be selected that contain at least 1 white ball?

Question

Section A1: List the elements of the set in roster notation. (Enter EMPTY or ∅ for the empty set.)    {x | x is a letter of the word TALLAHASSEE}2: Let A and B be subsets of a universal set U and suppose n(U) = 400, n(A) = 125, n(B) = 90, and n(A ∩ B) = 40. Find the number of elements in the set.  n(Ac)3: Let A and B be subsets of a universal set U and suppose n(U) = 400, n(A) = 125, n(B) = 80, and n(A ∩ B) = 60. Find the number of elements in the set n(Ac ∩ B4: Let A and B be subsets of a universal set U and suppose n(U) = 350, n(A) = 115, n(B) = 70, and n(A ∩ B) = 60. Find the number of elements in the set. n(Ac ∩ Bc)BONUS AEvaluate the quantity.  3 · P(5, 2) · C(9, 3) Section B1: The Department of Foreign Languages of a liberal arts college conducted a survey of its recent graduates to determine the foreign language courses they had taken while undergraduates at the college. Of the 500 graduates205had at least one year of Spanish.170had at least one year of French.141had at least one year of German.37had at least one year of Spanish and French.29had at least one year of Spanish and German.22had at least one year of French and German.4had at least one year of all three languages.(a) How many of the graduates had at least 1 yr of at least one of the three languages?(b) How many of the graduates had at least 1 yr of exactly one of the three languages?(c) How many of the graduates had less than 1 yr of any of the three languages? 2:  In how many ways can 9 different compact discs be arranged on a shelf?(a) In how many ways can four pictures be selected from a group of ten different pictures? 3: How many three-digit numbers can be formed from the numerals in the set {1, 2, 3, 4, 5} if the following is true?(a) Repetition of digits is not allowed(b) Repetition of digits is allowed4: Five soups, two entrées, and four desserts are listed on the &#34;Special&#34; menu at the Neptune Restaurant. How many different selections consisting of one soup, one entrée, and one dessert can a customer choose from this menu?BONUS BIn a survey conducted by Helena, a financial consultant, it was revealed of her 420 clients279 own stocks.192 own bonds.182 own mutual funds.115 own both stocks and bonds.98 own both stocks and mutual funds.96 own both bonds and mutual funds.How many of Helena's clients own stocks, bonds, and mutual funds? (Assume each client invested in at least one of the three types of funds.) Section C 1: In an election being held by the Associated Students Organization, there are eight candidates for president, three for vice-president, five for secretary, and six for treasurer. How many different possible outcomes are there for this election?2: There are eight seniors and five juniors in the Math Club at Jefferson High School. In how many ways can a math team consisting of four seniors and three juniors be selected from members of the Math Club? 3: From a shipment of 60 transistors, 3 of which are defective, a sample of 5 transistors is selected at random.(a) In how many different ways can the sample be selected?(b) How many samples contain exactly 3 defective transistors?(c) How many samples do not contain any defective transistors?  BONUS CA sample of 4 balls is to be selected at random from an urn containing 16 balls numbered 1 to 16. Six balls are green, 5 balls are white, and 5 balls are black.(a) How many different samples can be selected?(b) How many samples can be selected that contain at least 1 white ball?

Accepted Answer

Answered: Image /qna-images/answer/1cfa4f61-03f4-4dfa-9ac2-dd4186efba78.jpg

205	had at least one year of Spanish.
170	had at least one year of French.
141	had at least one year of German.
37	had at least one year of Spanish and French.
29	had at least one year of Spanish and German.
22	had at least one year of French and German.
4	had at least one year of all three languages.