Take Test: PW 10 (Sec 6.3, 6.4) * Test Information Description Instructions Multiple Attempts This test allows 3 attempts. This is attempt number 1 Force Completion This test can be saved and resumed later. Your answers are saved automatically . Question Completion Status: QUESTION 10 points Save Answer Evaluate : a ) P (10 , 7 ) = b) P (5, 3 ) = c) C(8, 6) = d) C(4, 1) = QUESTION 2 10 points Save Answer There are six different candidates for governor of a state. In how many different orders can the names of the candidates be printed on a ballot? QUESTION 3 10 points Save Answer How many subsets of cardinality 5 does a set with 12 elements have? QUESTION 4 10 points Save Answer How many bit strings of length 7 contain at least three 1s? O 35 O 99 O 29 10 QUESTION 5 10 points Save Answer How many bit strings of length 7 have at most three 1s? 35 29 O 64 99 QUESTION 6 10 points Save Answer How many permutations of the letters ABCDEFGH contain (a) the string ED? (b) the strings ABC and DE? (c) the strings ABC and CDE? (d) the strings ABC and BEF? QUESTION 7 10 points Save Answer Seven women and nine men are on the faculty in the mathematics department at a school. (a) How many ways are there to select a e department if at least one woman must be on the committee? (b) How many ways are there to select a committee of five members of the department if at least one woman and at least one man must be on the committee? QUESTION 8 10 points Save Answer How many ways are there for 5 men and three women to stand in a line so that no two women stand next to each other? [Hint: First position the men and then consider possible positions for the women.] Give your answer in numerical form. QUESTION 9 10 points Save Answer Which of the following is a coefficient of x in (2- x) 11? O -5280 O -330 330 O 5280 QUESTION 10 10 points Save Answer Use the binomial theorem to expand ( 3.x - y 2) 4 Show your work on paper, and then upload an image of your work using the button below. Attach File Browse Local Files Browse Content Collection Browse Dropbox Click Save and Submit to save and submit. Click Save All Answers to save all answers. Save All Answers Save and SubmitTake Test: TW 10 (Sec 6.3, 6.4) * Test Information Description Permutations and combinations Binomial coefficients Instructions Multiple Attempts This test allows 2 attempts. This is attempt number 1. Force Completion This test can be saved and resumed later. Your answers are saved automatically. Question Completion Status: QUESTION T 10 points Save Answer Choose all correct formulas to calculate r-permutations and r-combinations of n elements. O P(n, r) =r! P ( n, r) = - (n- r) ! P(n,r) =n(n-1) (n-2) ... (n-r+1) O C(n, r) =n! n! c(n, r ) = ?! ( 1- 1 ) ! c(n.r ) = QUESTION 2 10 points Save Answer A permutations of a set of distinct objects is an of these objects An ordered arrangements of r elements of a set is called an An selection of r elements from the set is called QUESTION 3 10 points Save Answer Permutation vs combination Which notation (permutation, r-permutation, or r-combination) would you use in each of the given problems? - Suppose that there are eight runners in a race. The winner receives a gold medal, the second- A. 5-combination inisher receives a silver medal, and the third-place finisher receives a bronze medal. Ho B. Permutation occur and there are no ties? s are there to award these medals, if all possible outcomes of the race can C. 4-combination - Suppose that a saleswoman has to visit eight different cities. She must begin her trip in a specific D. 3-permuations city, but she can visit the other seven cities in any order she wishes. How many possible orders E. 3-permutation can the saleswoman use when visiting these cities? F. 5-permutation - How many ways are there to select a first-prize winner, a second-prize winner, and a third- prizewinner from 100 different people who have entered a contest? G. 8-permutation How many poker hands of five cards can be dealt from a standard deck of 52 cards? QUESTION 4 10 points Save Answer Permutation vs combination Which notation (permutation, r-permutation, or r-combination) would you use in each of the given problems? - How many permutations of the letters ABCDEFGH contain the string ABC? A. 3-permutation How many ways are there to select a first-prize winner, a second-prize winner, and a third- B. Permutation prizewinner from 100 different people who have entered a contest? C. 5-permutation - How many ways are there to select five players from a 10-member tennis team to make a trip toa match at another school? D. 8-permutation A group of 30 people has been trained as astronauts to go on the first mission to Mars. How many E. 5-combination ways are there to select a crew of six people to go on this mission (assuming that all crew F. 6-combination members have the same job)? G. 3-combination QUESTION 5 10 points Save Answer How many bit strings of length 8 contain exactly four 1s? Select ALL that applies. 70 O S! 8! O 1680 O P(8, 4) O C(8, 4) QUESTION 6 10 points Save Answer From the list below select all terms of the binomial expansion of ( x+y )+. 0 3xy 0 ( 4) QUESTION 7 10 points Save Answer What is the coefficient of x 12y 13 in the expansion of (x+ y) 25? ( 25 13 O 12 O 13 O ( 13 12 QUESTION 8 10 points Save Answer What is the coefficient of x 12y 15 in the expansion (2r - 3y) 25? Select ALL that applies ( 25 13 25! 12:13 25 123 13 13 (2512 2 123 13 O 25! 12: 131 2123 13 Click Save and Submit to save and submit. Click Save All Answers to save all answers. Save All Answers Save and Submit