Explore BrainMass

Explore BrainMass

    Binomial coefficients and nonnegative integers

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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.

    © BrainMass Inc. brainmass.com December 24, 2021, 10:52 pm ad1c9bdddf
    https://brainmass.com/math/discrete-structures/binomial-coefficients-nonnegative-integers-514202

    SOLUTION This solution is FREE courtesy of BrainMass!

    Hello there,

    The solution is attached. I made sure to double check everything for errors and typos.

    P.S I used the famous document preparation system LaTeX so that all the math symbols show up nicely.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 10:52 pm ad1c9bdddf>
    https://brainmass.com/math/discrete-structures/binomial-coefficients-nonnegative-integers-514202

    Attachments

    ADVERTISEMENT