For the following permutations, find the number of inversions: Show your solution. a. 467918352 b. 35728614 c. 4573612 d. 58271364e. 641597283
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- Answer the following questions. 4. Describe how the permutation of ii objects differs from the permutation of choosing r objects from a set of n objects. Include how each is calculated.Find the number of inversions in each of the following permutations of S = {1, 2, 3, 4, 5}: (a) 13542 (b) 35241 (c) 12345Get the 1st order DE of the following:
- In part B, how was 0.5 obtained?Show that the permutations (12) and (12345) generate S5.Nationally, at least 60% of Ph.D. students have paid assistantships. A collegedean feels that this is not true in his state, so he randomly selects 50 Ph.D.students and finds that 26 have assistantships. At α = 0.05, is the deancorrect?
- How many arrangements are there of the letters of the word CHEESECAKE under each condition? When repetition is allowed? When arrangement starts with A? When the four E’s are to be together?For the following three questions answer with a decimal rounded to the nearest hundred thousandth (5places after decimal). a) If 3 random cards are drawn without replacement from a standard deck, the probability that all the cards are hearts is [cards1]. b) The probability that all the cards are face cards is [cards2].Note: Face cards are kings, queens, and jacks. c) The probability that all the cards are even is [cards3].(Consider aces to be 1, jacks to be 11, queens to be 12, and kings to be 13.)G is defined as this fair spinner landing on a multiple of 4. H is defined as the spinner landing on 11 or higher. What is P(G AND H)? Give your answer in decimal form.
- If N = 18 and α = 0.052 tailed, the value of Tcrit is _________.This is discrete math. Question 1. What is the difference between a permutation and a combination? Question 2. Discuss why the number of subsets on an n-set is equal to 2 n .Find the value of p(x,4)and p(x,6) using permutation formula where x is the 09.