Letr be a real number and let k be an integer. We then define the binomialcoefficient () by=r(r-1)(r-k+1)k!0if k 21if k = 0if k ≤ -1. 1. For any real number r and any integer r #k, show that a) ()=(¹), and b) () =(-1)k (r+k-1). Hint: use the definition of () from Page 137.r-k

The Binomial coefficient is defined as: rk=rr-1...r-k+1k! for k≥1 k is an integer and r is a real…

Answered: Letr be a real number and let k be an…

Letr be a real number and let k be an integer. We then define the binomial coefficient () by (3) r(r-1)(r-k+1) k! 1 0 if k 21 if k = 0 if ks-1.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

b. For each positive integer n, let P(n) be the property 5* – 1 is divisible by 4. Write P(0). Is P(0) true? ii. Write P(k). iii. Write P(k + 1).
Evaluate (z – 2)(z² + 9)
which pair of binomials disproves Eric's ㅇ (z-2)(z + 3) ㅇ (z-2) (z + 2) z+3)(3 2)
1. In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 56.4 inches, and standard deviation of 4 inches.A) What is the probability that a randomly chosen child has a height of less than 46.7 inches?Answer= (Round your answer to 3 decimal places.)B) What is the probability that a randomly chosen child has a height of more than 57.5 inches?Answer= (Round your answer to 3 decimal places.) 2. In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 55.1 inches, and standard deviation of 6.3 inches. What is the probability that the height of a randomly chosen child is between 62.05 and 66.85 inches? Do not round until you get your your final answer, and then round to 3 decimal places. Answer= (Round your answer to 3 decimal places.) 3.
Expand the following binomial powers.
Identify the coefficient of x5 in the Binomial Theorem expansion of (2x - 5)12 . Group of answer choices C(12,7) 25 57 - C(12,7) 25 57 - C(12,7) 25 57x5 None of these. C(12,7) 25 57x5
Note: The integer functions P(m,n) and C(m,n) are available for use. Use the binomial theorem to expand the following expressions. a. (1+x)7 b. (x+w)6 c. (x-w) 6 If you don't get this in 2 tries, you can get a hint.
Let -6 M = Find formulas for the entries of M", where n is a positive integer. Hint: a formula such as 5 · (2.3) + 7· (3.5)" is typeset as 5*(2.3)^n+7*(3.5)^n.
Use the Binomial Theorem to expand and simplify the expression. (x² + y?)4 Select one: O a. x8 + 6x6y² + 4x*y* + 6x²y6 + yô O b. x8 + 6x5y² + 4x*y4 + 4x²y6 + yô Oc. x + 4xfy2 + 6x*y* + 4x²y% + y° + y° O d. 3x + 2xy² + 9x*y* + 4x²y% + 2y8