Show that                               n                    n                    (            )  =    (              ).                               k                    n - k Give an interpretation involving subsets.

Question
Asked Sep 8, 2019

                               

Show that     

                          n                    n

                    (            )  =    (              ).     

                          k                    n - k

 

Give an interpretation involving subsets.

    

check_circleExpert Solution
Step 1

To interpret (hence prove) the given equality of the two binomial coefficients, using set theory

Step 2

First let us look at an example; the same proof will apply to the general case. In the example, n is 5 and k is 2, n-k is 3. The left hand side is the number of subsets of 2 elements from a set of 5 elements. Every time w...

Let n 5,k 2
Then the given equality is
5
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Let n 5,k 2 Then the given equality is 5

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