3. For the following permutations, find the number of inversions: Show your solution. a. 467918352 b. 35728614 c. 4573612
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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) 12345In which of the following arrangements are the numbers placed in increasing size order?
- Get the 1st order DE of the following:If the n objects in a permutations problem are not all distinguishable—that is, if there are n1 of type 1, n2 of type 2, and so on, for r different types—then the number of distinguishable permutations is given by n!n1!n2!•••nr!. How many permutations are possible using the 11 letters in the word MISSISSIPPI?Which of the following numbers could be the exact number ofelements of order 21 in a group: 21600, 21602, 21604?
- 1. Use the example above to deduce Gauss's theorem for the first 99 counting numbersHow 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?"When we are considering n objects taken r at a time, with r . 1, why will the number of combinations be less than the number of permutations?" - for this question, I can not visualize what they are asking. Is this means a number of combination would be the less than a number of permutation because r is in the denominator?
- What conditions on w, x, y, and z will guarantee that we can find a, b, c, and d so that the following is a valid addition table?Show that the permutations (12) and (12345) generate S5.Is there a formula or way to determine how many transpositions there are for a cycle of a given length? Is there a bound of sorts on the minimum and maximum number of transpositions for a cycle of a given length? For example, suppose I have a cycle of length 5. I know there are only an even number of transpositions possible, but how many are there actually? Wouldn't the smallest number be 4 transpositions for a cycle of length 5? I know there is one with 6 transpositions possible for a cycle of length 5? Are there others? If so, can we determine them? Is it correct to say that if a permutation is a 5-cycle, then it has 2s number of possible transpositions?