Question: please do fast!! i will rate you good for sure!!! 18. Consider two natural numbers n,k and p where 0 S k S p S

please do fast!! i will rate you good for sure!!!

18. Consider two natural numbers n,k and p where 0 S k S p S n a. Prove that: P(n + 1, k) = POI, k) + kP(n, k 1) b. Prove that:C(n, k)C(n k, p k) = C (p, 106' (n, p) c. Find the sum of S where p n n k S _ Z (k) (p - k) k=0 (1. Find a number n Where n 2 3 such that (at) + (g) + (2) = 5n

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

please do fast!! i will rate you good for sure!! Exercise 4. Suppose that the weather (either wet or dry} tomorrow will be the same as the weather today with probability p F. [0,1]. (:1) Show that...

please do fast!! i will rate you good for sure!! 1. Two Zonlbie Dice are rolled. Let. E be the event. that one Brain is obtained and F be the went. of at least one Shotgun is obtained. List the...

HW 12, MAT 312/AMS 351: SPRING 2017 Problem 1. (1) Set H = {4a + 6b | a, b Z} Z. Show that H is a subgroup of Z. (2) Is H cyclic? Problem 2. Write down all the cyclic subgroups of the following...

In this question you will be asked to reflect on a project you have been involved in or observed, in which a design evolved, or could have evolved, through applying a theory of user behaviour. You...

In a Hopfield neural network configured as an associative memory, with all of its weights trained and fixed, what three possible behaviours may occur over time in configuration space as the net...

Consider the trigonometric series a0 2 + X r=1 (ar cos rx + br sin rx) where a0, a1, a2, . . . and b1, b2, . . . are constants and suppose that f(x) is a periodic function of x with period 2. (a)...

ttth Suppose that the sequence of bags {Bn | n N} is recursively enumerated by the computable function e(n, x) = fn(x), [7 marks] Hence prove that the set of all recursive bags cannot be recursively...

In this question assume that p and q are atomic formulae. (a) Compare and contrast path formulae and state formulae in temporal logic. [4 marks] (b) Describe and contrast the meanings of F(G p) and...

Explain why, on a busy system, key press echoes might be delayed when a high-priority user interacts with a low-priority application. Propose a solution, describing how each of the above system calls...

"Fortran, Algol and Lisp invented most programming language concepts 50 years ago; adding the concept of object-orientation suffices to explain all programming languages to date". To what extent is...

Mathews Company exchanged equipment used in its manufacturing operations plus $6,000 in cash for similar equipment used in the operations of Biggio Company. The following information pertains to the...

In Exercises 17-30, either prove that the wff is a valid argument or give an interpretation in which it is false. 17. (3x)[A(x) ^ B(x)] (3x)4(x) ^ (3x)B(x) 18. (3x)[R(x) V S(x)] (3x)R(x) V (3x)S(x)...

Considering the importance of liquidity and profitability in current asset management, how can a company effectively balance the need for sufficient liquidity to cover short - term obligations with...

Given the following data on a hardware item stocked by Andreas Wieland's paint store in Copenhagen, should the quantity discount be taken? D=1,210 units; S=$40; H=$2; P=$9 Discount price=$6.75...

11. Now consider the different goals you have for your life in the future. See these goals in relation to your core values and your roles. How do goals affect your roles and your values? Development...

Does this future have a sound, an image, a taste or a smell that you can evoke here and now?

2. In this chapter, the reader should reflect on the following concepts: benchmark-ing, competence development, thought dispositions, identity and perception.