MA 37500 Study Guide - Midterm Guide: Binomial Coefficient, Fibonacci Number, Without Loss Of Generality
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How many ways are there to permute aabbccdd such that the upper case letter. However, if we now regard that the upper case letter must come first, we note that there are 4 upper case letters and that there are 2 ways to permute it with its respective lower case letter (eg 2! Now, we have already considered before the case of when we are choosing r from. Now, let"s consider something right before n many choices. It would be rn ( 1 n. Now, that aside, we"ve considered before something like ( + y 10 x. This is such a pain to write out if we don"t have binomial coefficients. It tells us n ( + y n = x k=0. C r (n, ) x y k n k. Let"s consider an example in light of this! ( + y n = y10 + 1 x. Pascal"s identity comes in quite handy when it comes to doing combinations.
