Binomial coefficients and nonnegative integers

Assignment Help Mathematics

Reference no: EM13131441

Prove the identity (n~r) (r~k) = (n~k) ((n-k)~(r-k)), whenever n, r, and k are nonnegative integers with r less than/equal to n and k less than/equal to r:

a) Using a combinatorial argument.

b) Using an argument based on the formula for the number of r-combinations of a set with n elements.

Reference no: EM13131441

Questions Cloud

Describe how you to simulate rolling the dice : You are one space short of winning a child's board game and must roll a 1 dice to claim victory. You want to know how many rolls it might take. Describe how you would simulate rolling the dice until you get 1.

Calculate the optimal amount of pretzels : Calculate the optimal amount of pretzels and soft drinks that minimizes this firm's costs and how many frames do you provide each month?

Compute kelly taxable income : Kelly is single. Her dependent child, Barbara, lives with her. After her divorce, Kelly was awarded the permanent custody of Barbara and has not agreed to waive her right to claim Barbara as a dependent. Kelly has the following items as income and..

What is the ph of a solution : What is the pH of a solution that is 0.75 M in sodium acetate and 0.50M in acetic acid? (Ka for acetic acid is 1.85 x 10-5).

Binomial coefficients and nonnegative integers : Prove the identity (n~r) (r~k) = (n~k) ((n-k)~(r-k)), whenever n, r, and k are nonnegative integers with r less than/equal to n and k less than/equal to r:

What mass of nitrogen is obtained : Gas ammonia can be decomposed to give 3.00 by mass of hydrogen and 14.0 by mass of nitrogen.what mass of nitrogen is obtained.

Triethylamine and water explain the measurement of the ph : What is the pH of 10 drops of triethylamine in a dropperful of demineralized water? How does the reaction between triethylamine and water explain the measurement of the pH?

Confidence interval for population mean cash value of crop : A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop. What is the margin of error?

Determining squarefree numbers : An integer is called squarefree if it is not divisible by the square of a positive integer greater than 1. Find the number of squarefree positive integers less than 100.

User Account

All Pages