Find all 6 permutations of (12)(345).

Q: Compute f2,f3, and f-1 for each of the following permutations.   f= (1,5,2,4)

A: Given: f=(1,5,2,4) To determine the f2 f3 f-1

Q: 16. The expansion of (2 + 3x;-1 is valid when >x>

A:

Q: 26. In how many ways can up to 4 students be selected from 6 girls and 5 boys if each selection must…

A:

Q: A box contains five cards with even numbers and seven cards with odd numbers. If two cards are drawn…

A: Given : n (even) = 5 n (odd ) = 7 n (total) = 5 + 7               = 12 number of cards drawn with…

Q: Evaluate the permutation. 6P₁= X S

A: nPr=n!/(n-r)! Where  n!=n(n-1)(n-2)..3x2x1  n!=n(n-1)!

Q: The first term of the expansion of (j – 3n)a is –-3nª. True or False?

A: The \displaystyle \left(r+1\right)\text{th}(r+1)th term of the binomial expansion of \displaystyle…

Q: 1. Compute the value of (), for n > 3.

A: Formula: nr=n!r!n-r!

Q: Determine the coefficient of at in (1 – 4a²)ó by completing the following given steps.

A: Concept:

Q: Let r(n) be the number of n-permutations whose square is the identity permutation. Prove that if n >…

A:

Q: Write the permutation corresponding to R90 in the left regular representationof D4 in cycle form.

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Q: Find f (n) when n = 4k, where f satisfies the recurrencerelation f (n) = 5f (n∕4) + 6n, with f (1) =…

A:

Q: Compute P (Z < -1.32).

A: Z-score = -1.32

Q: Compute f2,f3, and f-1 for each of the following permutations.   f= (l,3,7,4)(2,5,9,8,6)

A: f= (l,3,7,4)(2,5,9,8,6)

Q: THEOREM 2.4 The number of distinct permutations of n things of which n1 are of one kind, n2 of a…

A: Given: Theorem 2.4 and Theorem 2.5

Q: Find a closed formula for a, if ak = 5n² + 4n k=1 an =

A:

Q: Use the permutation and combination formulas to prove the following. +k – 1) (n + k – 1 (b). V k, n…

A: We have to  prove given formula using peemutation and combination

Q: 7) Show that for any permutations a and ß in Sn, a*ß and ß have the same parity.

A: We have to show that a4b and b have same parity in the group.

Q: Compute f2,f3, and f-1 for each of the following permutations. f= (2, 7,4,3,5)

A: Given: f= (2, 7,4,3,5) To Compute: f2,f3, and f-1

Q: Express the permutation (2 4 5)(1 3 5 5)(1 25) as a single cycle or as a product of cycles.

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: SHOW THE FULL SOLUTION OF THIS PERMUTATION 3!

A: Given3!

Q: Prove the following using the binomial theorem: ()=()+ 2n

A: In this context, the aim is to prove 2n2=2n2+n2.

Q: Use the permutation and combination formulas to prove the following. (a) For all integers n 2 2,…

A: We will solve the problem

Q: Find the ordinary generating function for the number of partitions of n in which no part occurs more…

A:

Q: Show that n is composite if and only if p(n) <n – Vn.

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Q: Use the binomial theorem to prove (2n choose k ) x  2^(2n-2k)= (2.5)^2n

A:

Q: 2. Let f and g be any permutations. Show that the order of h = fgf- is the same as the order of g.

A: Here f and g are tow permutations  and we are given that h=fgf-1. We have to show that both f and g…

Q: 2X+3=1 mod 5 Show your work

A: We have solve given problem:

Q: Compute |A| for the following:

A: Given, we have to find the determinant of A

Q: If a and b are relatively prime then alb

A: Given below the detailed solution

Q: Let r(n) be the number of n-permutations whose square is the identity permutation. Prove that if n >…

A:

Q: Which of the following statements are true about the recurrence relation: yk + yk+4 + log (yk-2)=k2?…

A: A recurrence relation is defined when the value of a term of the series is dependent on other terms…

Q: (8) Prove that if A and B are similar, then their transposes are also similar.

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Q: Use any method to deter (a) 13 The series 8.

A:

Q: Let m and n be positive integers and let k be the least common multipleof m and n. Show that mZ∩ nZ…

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Q: Compute the following: N!(N-4)!

A: Note that n!=n×n-1×n-2×…×3×2×1. Consider the given expression N!N-4!. This can be written as…

Q: Show the p in th

A: Vertices of the triangle is Given integral is

Q: 2. Prove that Qn [2, 3] ~ N.

A: Two sets A and B have the same cardinality if there exists a bijection (onto , one-to-one…

Q: Let a1 = a2 = 1 and suppose an = an-1 + an-2 for n ≥ 3. Prove that a1a2 + a2a3 + · · · + a2n-1a2n =…

A: We have given that , a1 = a2 = 1 Also , an = an-1 + an-2 We need to prove that ,  a1a2 + a2a3 +…

Q: Prove that ℤ/n has exactly n elements.

A:

Q: (j) Find a recurrence relation for the r

A: Recurrence relation:

Q: Show that Zn has a nonzero nilpotent element if and only if n is divisibleby the square of some…

A:

Q: compute the following in Z12: [9]+[11], [5]-[8], and [7][9].

A: Consider the provided question, We have to find the following in z12:9+11, 5-8, and 79 Find,…

Q: even and n > 4, show that rk is an element of order 2 which commutes with all elements of D2n

A: Given, n = 2k is even and n ≥ 4, We have to show that rk is an element of order 2 which commutes…

Q: Suppose that there are n = 2k teams in an eliminationtournament, where there are n∕2 games in the…

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Q: Find the term independent of x in the expansion of 3 1 - 2r

A:

Q: n! diverges because an > 0. for alln2 1. True False

A:

Q: In a Wilcoxon Mann Whitney test n1 is 9 and nprime is 7. What are the correct values for K1 and K2 ?…

A: In a Wilcoxon Mann Whitney test n1 is 9 and nprime is 7.  We need to find the correct values for K1…

Q: 4. Prove that the L{2t²} = 4 S3

A:

Q: A certain sample of E. Coli has 2.5 times the population every hour. If the sample began with 50…

A: Given, A certain sample of E. Coli has 2.5 times the population every hour If the sample began with…

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.