4 5 1 f = 4 2 3 6 7 3 6 2 7 1 (a) Write f as a product of transpositions (not necessarily disjoint), separated by commas (e.g. (1, 2), (2, 3),... ). f = (b) Write f- as a product of transpositions in the same way. f-1 = %3D Assume multiplication of permutations f,g obeys the rule (fg)(x) = f(g(x)) so (1, 3)(1, 2) = (1,2, 3) not (1,3,2).

Q: Assume the cards are drawn sequentially and without replacement. (permutations) In how many ways…

A: Given data, given that 5 Spades can be drawn from a standard deck of 52 cards. The cards are drawn…

Q: Show that An (B U C) = (Ñ n B) u Ā - Using membership tables.

A: Solution:

Q: . How many 4-membered subsets can be chosen from {1, 2, 3, 4, 5} if repetitions are allowed?…

A: Number of ways to choose r numbers from a n -set is nCr

Q: Find the intersection between the set of all integers bigger than 0 but smaller than 10 and the set…

A:

Q: Prove that if five cards are randomly chosen from an ordinary 52- cards deck, at least two cards are…

A:

Q: Let S=(1,2,3,4,5,6,7,8). How many permutations are there if: a. The odd and even numbers trade…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 6g= 3 1 2 3 3 6 * 2 3 2 2 3 ス 3 ス 2 2 3 3

A:

Q: 5. How many 2-permutations are there of a set of eight objects?

A: We know that,  The formula pf permutations is,  nPr = P(n, r) = n!/(n-r)!

Q: Identify the notation used for each of the following concepts. a. k factorial b. The number of…

A: a. k factorial is denoted as k!

Q: Let A = {1, 2, 3, .. ., 12} and let p.rand q permutations on A defined by p=(2,10,11), r= (3,6,5)…

A:

Q: Counting Permutations A permutation of the set [10] = {1,2, 3, ., 10} is a way of listing the…

A: Given set is 10=1,2,3,...,10 To find how many permutations of 10 start with k, k-1, k-2, ....,1 for…

Q: Consider a permutation of the first n positive integers. For example, if n = 10, then a possible…

A:

Q: A(n) _______ is an ordered arrangement ofr objects chosen from n objects.

A: We fill the blank space as

Q: Given the following function values, use the Trapezoidal Rule with five function values to…

A:

Q: The following table shows the total student enrollment at a certain university for the years 2001…

A: ∵ Given that Year Enrollment 2001 5621 2002 5687 2003 5805 2004 5783 2005 5758

Q: Prove that n! (n-r)!r! (4) is the number of subsets (combinations) with r elements which can be…

A:

Q: Consider the following permutations in S;: (1 2 3 4 5 6 7) 6 2 4 1 7 5 3) (1 2 3 4 5 6 7 4 3 2 7 1 5…

A:

Q: Use inclusion-exclusion to find the number of ways to arrange the six numbers 1, 2, 3, 4, 5, 6 such…

A: please see the next step for solution

Q: Let f and g be permutations on the set {1, 2, 3, 4, 5, 6, 7, 8, 9}, defined as follows f = (31…

A:

Q: Is a permutation of one element considered to be an even permutation? For example, is (1) an even…

A: To clarify the notion of an even permutation

Q: 2. even numbers are in their natural positions. Determine the number of permutations of {1, 2, 3, 4,…

A: Here we use combination rules. And set theoretic rules.

Q: How many inversions are in the following permutation?: [2, 5, 1, 6, 3, 4]

A: Inversions of a permutation

Q: How many permutations of {1,2,3,4,5,6,7} have exactly one element fixed?

A: Using inclusion-exclusion principle to compute the given permutation: There are 71·6! ways to select…

Q: Every permutations can be expressed as a   product of transpositions.

A:

Q: Let ? and ? be permutations on the set {1,2,3,4,5,6,78,9}, defined as follows

A: Introduction: A permutation is a bijective mapping from a set to itself. The general way to…

Q: Is A a subset of B if A = {2, 3, 5, 7, 8, 9, 10} andB = {3, 5, 8, 9}?

A: The given sets are, A=2,3,5,7,8,9,10B=3,5,8,9 A set A can be said to be the subset of another set B…

Q: How many 3-element subsets of (0, 1, 2, 3, 4, 5, elements sum to odd integer? C(5, 3) + C(5, 1) x…

A: There are 5 even ξ 5 odd numbers in the given set. We know that sum of any number of even numbers is…

Q: Show that the set {2, 5, 8, 11, 14, . . . } is infinite.   Group of answer choices: Choose answer…

A: Topic-series

Q: Let X = the number of nonzero digits in a randomly selected 4-digit PIN that has no restriction on…

A: We have given that  Let x = the number of non zero digits in a randomly selected 4 digit PIN that…

Q: Consider the following permutations in S7: (1 2 3 4 5 6 7) "- (6 2 7 5 4 1 3) The order of ß is (1 2…

A: Consider the given permutations  α and β. We need to find the order of  β. The solution is given…

Q: 4. Count the permutations 111213141516 of 1, 2, 3, 4, 5, 6} where i • 12 #1 i3 #1 1,2,3 i5 5,6 i6 #…

A: count the permutations  i1,i2,i3 i4,i5,i6 of  1,2,3,4,5,6 where i1≠1,2,3 i2≠1 i3≠1 i5≠5,6 i6≠5,6