Show the following using factorials: k k- 1

Q: In a “Pick-4” game, a player wins a prize for matching a 4-digit number from 0000 to 9999 with the…

A: Given: A player wins a prize for matching a 4-digit number from 0000 to 9999 with the number…

Q: Examine the properties of the operation o defined by the equation xoy= x2+y2 in the N natural…

A: Given: The equation x∘y=x2+y2 in the N natural numbers set

Q: The prime f actorization of 7007 is

A: 7007=7×1001       =7×11×91       =7×11×13×7       =72·11·13

Q: Let p > 5 be the prime number. Prove that the expression p – 10p +9 is divisible by 1920.

A: We have to prove that the expression p4-10p2+9 is divisible by 1920.

Q: Let (") denote the binomial coefficient (also written as C(n, r) or nCr). Then (,",) + (;) =

A:

Q: Find the largest value of n such that: >(3k - 8) < 2021. k=1

A: NOTE: Refresh your page if you can't see any equations. .

Q: b. Assume prior studies have shown that about 55% of full-time students earn bachelor's degrees in…

A: We have given that  95% confidence interval then alpha=0.05 Margin of error=E=0.04 Zc=1.96 at…

Q: 2k > 1+ k

A: We have to prove 2k ≥ 1 + k for every natural number k

Q: How many 12-digit numbers have all their digits in nondecreasing order? For example, 266888 is a…

A: Let the twelve digits be d1,d2,d3, d4,d5,d6,d7,d8,d9,d10,d11,d12 from left to right. Let a1=d1…

Q: In (Z24, €) find the orders of the elements 3, 4, 6, 7, and 18.

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: 5 У32 — х

A:

Q: 3 for all n.

A: We have to find the following conditions according to the given information

Q: Find the value of the permutation 2Pi

A:

Q: a. Assume that nothing is known about the percentage of passengers who prefer aisle seats. n= (Round…

A: a. The percentage of of passengers who prefer aisle seats is not known consider as 0.5, 99%…

Q: How many 4-digit numbers have all their digits in nondecreasing order? For example, 266888 is a…

A: Solution:- In the given problem, we will find how many 4-digits number have all their digits in…

Q: Use Pascal's triangle to expand the binomial. 6 (d– 5y)º

A:

Q: Using the digits 0 through 8, find the number of different 5-digit numbers such that: Digits can be…

A: Hey, since there are multiple sub-parts posted, we will answer first three sub-parts. If you want…

Q: The following figure shows a factorial design with Factor A having 2 levels and Factor B having 3…

A: Factorial ANOVA

Q: Expand the binomial by using Pascal's Triangle to determine the coefficients. (x - 2y)5

A:

Q: ress the following using factorials and simplify:

A:

Q: If p is a prime number greater than 3, which of the following represents the sum of the positive…

A: we will check all the options to ensure which is correct.

Q: Use the binomial theorem to prove that 2^k * "n choose k"  =. 3^n.

A: Binomial theorem: The statement of binomial theorem is given below:

Q: Write the following expression without using the factorial symbol (n-4)!/(n-1).    A.…

A: Known fact: n!=1×2×3×…×n-1×n

Q: Evaluate the factorial expression. (n+ 2)! n!

A: The evaluation is as below

Q: Find the value of (99)^4 (using the binomial theorem).

A: This question is related to binomial theorem

Q: Kerys is trying to expand the binomial (2x +y)* using the binomial theorem expression, a"-*b* What…

A: Given:      Binomial 2x+y4 The binomial expansion theorem states that            a+bn=∑k=0nnCkan-kbk…

Q: Evaluate the factorial expression.

A: Given:               n+2!n!   n+2!=n+2×n+1×n×n-1n-2........3×2×1 n!=n×n-1n-2........3×2×1

Q: Find the value of the factorial. 7! 7! = (Type a whole number.)

A: In this case, we need to find the value of factorial of 7.

Q: 2. Derive the following binomial identity: (n + () --("-") = r

A: To derive the binomial identity; n+1rn+1=rr-1n We have to prove that the left hand side of the…

Q: What is the row of Pascal's triangle containing the binomial coefficients (), 0 < k < 9?

A: The first row of pascal triangle contains only one element i.e. 1. In second row, there are two…

Q: What is the coefficient of p5q5 in the expansion of (p+q)10?

A:

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: 11. Explain what is a factorial and show an example of how to compute it.

A: A factorial of a number is the product of all positive integers less than or equal to the given…

Q: b. Assume prior studies have shown that about 40% of full-time students earn bachelor's degrees in…

A: It is given that margin of error (E) is 0.05 and the confidence level is 0.90.

Q: Determine the coefficient of a10 in (1 – 3a5) by completing the following given steps.

A: Since, you have post the multiple question. I am  answering first one. Please post again for the…

Q: Suppose that 56 % of students play football, 53 % of students play cricket, and 12 % of students…

A: Let F=students play footballC=students play cricketGiven,P(F)=0.56P(C)=0.53P(F¯∩C¯)=0.12

Q: Using the digits 0 through 8, find the number of different 5-digit numbers such that: (ANSWER…

A: While selecting the cases if the order of the selection matters then it is considered as permutation…

Q: I am trying to figure out how to make a know-show table for the question If m is an even integer,…

A: We can make a know-show table for the given condition.If m is an even integer, then the expression…

Q: Find the big O of the function ƒ(n) = n²" +n"

A: For (a), We are given the function f(x) = 3x2 - x - 1. We need to show that f(x) is O(x2) by finding…

Q: b) Assume that a recent survey suggests that about 82% of adults have heard of the brand. n = (Round…

A: Given that: Margin of Error=E                          =7%                          =0.07 The…

Q: Please Prove whether it is True or False. The value of nª - n² is divisible by 6 for any integer…

A: To prove that whether the given statement is true or false

Q: b) Assume that a recent survey suggests that about 77% of adults have heard of the brand. n = (Round…

A: here given for part b) sample proportion =  0.77  confidence level = 80% MOE  =  0.05

Q: Using the Binomial Theorem, show that n n n2"-1 k=0

A: Given: Let us determine the given, ∑k=0nknk=n2n-1using the binomial theorem.

Q: Find the next two terms in (an)n20 beginning

A: Given,             3,  5, 11, 21, 43, 85, . . .

Q: 2 ) + ("**) = n²- .2 2

A:

Q: Find 3 values of n such that phi(n)= 120

A: According to the given information, it is required to determine the values of n such that: