Write down all even permutations of {1,2,3,4} which take the element 1 to 2.

Q: 3. Find the number of distinct permutations that can be formed your ID number.

A:

Q: Find the number of distinguishable permutations of: 3 Cs, 6 Is, and 2 Ms

A: We have letter C 3 times, letter L 6 times and letter M 2 times.

Q: If the first three Fibonacci numbers are given as x, = 1, X2 = 1 and x3 = 2, then what is the least…

A: This is a question of number theory therefore from the subtopic of counting.

Q: 4, and 6 if no digit is repeated in any number? a. b. repetitions are allowed?

A: We have to find the number of two digit numbers.

Q: what

A:

Q: In a particular state, all automobile license plates consist of two capital letters (from…

A:

Q: In how many different ways can 7 bicycles be parked if there are 5 available parking spaces? 2.…

A:

Q: Show that im n /-

A: Limit of the sequence

Q: Let $n$ be a positive integer. Among C(2n,0),C(2n,1),..., C(2n,2n), C(2n,n) is the largest. True…

A:

Q: Show that 3n^ 2+8nlogn is big-Oh (n ^2 )

A:

Q: 3. Show that ifn = 2 (mod 4), then 9" + 8" is divisible by 5.

A: Here we will prove the given statement.

Q: A code have 4 digits in a specific order. The digits are between 0-9. How many different…

A: Code = 4 digits No. of available digit = 10 Repetition = not allowed Order is important, so we will…

Q: Can you give me an example of What is Permutations Rule (when all of the items are different?

A: Permutation rule:There are n different items and r number of selections and the selections are made…

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

A: Find all permutations with 12 in the first pair of bracket : (12)(345) (12)(354) (12)(435) (12)(453)…

Q: Find the number of permutations of the letters of these words:

A: Here permutations of word committee

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: Find the number of permutations using four different numbers (2,5,11,30) if they are taken 2 at a…

A: Given that, Four different numbers are (2,5,11,30) To find: Number of permutations using four…

Q: In how many distinct ways can the digits in the number 1,238,229,168 be arranged?

A: We have to find in how many ways the number  1,238,229,168 can be arranged.

Q: 2. Let, a, = 3, az = 4 and for n 2 3, a, = 2a,-1 + an-2+ 5, express a, in terms of n.

A: Topic:- series sum

Q: A cosets of of 212 are اخترأحد الخیارات + 2, +1,.1 O + 1,.2 O + 4, + 1, .3 + 4, + 2, + 1 , .4 O

A: Cosets Definition: Let G be a group and let H is a nonempty subset of G. A left coset of H in G is a…

Q: show that number of 132- avoiding permutations are equal to number of 123-avoiding permutations

A: We have to show that number of 132- avoiding permutations are equal to number of 123-avoiding…

Q: A1,...,A13 are thirteen different subsets of {1,2,3,4,5,6,7,8,9,10}. If each Aj has 6 elements for…

A: We are given that A1, ... , A13 are thirteen different subsets of {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.…

Q: What is Permutations Rule (when all of the items are different?

A: Introduction:Suppose there are n items; all the items are different from each other, that is, the…

Q: Find the number of permutations without replacement that can be created by drawing 5 balls from a…

A:

Q: Show that if there are 8 people in a room, then at least two of them must have been born on the same…

A: There are 7 days in a week.  So we can have 7 people who can have different birthdays from Sunday to…

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: With 100 candidates, find the number of permutations that can be made if 10 beauty queens are…

A: Given total number of candidates, n                 n = 100  Number of beauty queens that are to be…

Q: Find the number of distinguishable permutations of: 6 Ds, 5 Js, and 2 Os

A: our objective is to find the no. of permutations

Q: How many subsets of set S = {1, 2, 3, 4, 6} do not contain odd numbers? Use bijection to solve this…

A: Solution S={1,2,3,4,6}

Q: 1. Show that for n, mEZ", mEZ*, ged (2^-1,2m-)= 2 ged(n, m)_I

A: Suppose, in general, if p=gcdn,m then p=nx+my for some integers x, y Now if d=gcd2n-1,2m-1 then…

Q: Find the number of distinguishable permutations of the digits of the number 228,434.

A: Write the number in frequency format: Numbers Frequency fi 2 2 8 1 4 2 3 1 Total…

Q: Find the number of permutations x1, x2, x3, x4, x5,  of numbers 1, 2, 3, 4, 5 such that the sum of…

A: A number is divisible by 3 when one of the factors of the number is 3. Thus the sum…

Q: Calculate the least residues modulo 5 of 14, 24, 34, and 44.

A:

Q: Suppose there are 30 characters on a line which included A, B and C. If there are 9A, 14B, and 7C.…

A: We have to find no. Of permutations.

Q: How many three digit passcode can be made from the digits 0-9in the first number is not allowed to…

A:

Q: How many numbers must be selected from the set {1, 2, 3, 4, 5, 6, 7, 8} to guarantee that at least…

A:

Q: How many different words can be formed with the letters of the word ‘SUPER’ such that the vowels…

A:

Q: How many 6-permutations of [15] have their digits in increasing order?

A: Permutation is a technique to obtain the possible arrangements of listed items in a linear order.…

Q: How many ways are there to permute the elements of the multiset {1,1,2,2,3,4,5,6} so the first and…

A:

Q: Find the number of distinguishable permutations of: 5 As, 3 Gs, and 4 Ns

A: The answer is, 27720   The detailed solution is as follows below:

Q: 13. Determine the number of permutations of {1,2, . , 9} in which at least one odd integer is in its…

A: Solution : There are total 9 numbers from which five numbers  are odd (1, 3, 5, 7, 9) and four are…

Q: Find the number of distinguishable permutations of the letters in the word moon. List all the…

A: Total distinguishable permutations : moon Total letter in initial word = 4 Total o's = 2 So, total…

Q: A box contain 8 red and 6 green balls. In how many ways can 3 balls be drawn such that 2 is ed and 1…

A: Answer - A box contains 8 red and 6 green balls.                 How many ways can 3 balls be drawn…

Q: . Find the number of permutations of the letters of the word ‘REMAINS’ such that the vowels always…

A: We can solve these questions using given details

Q: Consider the set {1,2,3}. i. Write the elements of the permutations by taking two digits from above…

A:

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

A:

Q: How many permutations of all the letters in the English alphabet contain the string abc and the…

A: There are 26 letters in the English alphabet

Q: How many permutations of the 26 letters (English alphabet) do not contain any of the strings zero,…

A: Total number of permutations of 26 letters  (N) = 26! Number of permutations in which ZERO always…

Q: Suppose each license plate in a certain state has one digit, followed by four letters, followed by…

A: Given, Each license plate in a certain state has one digit followed by four letters followed by one…

Q: How many permutations of {1, 2, 3, 4, 5, 6, 7, 8) leave exactly 1 element fixed?

A: