Using double counting technique prove that p (n,p) is n(n-1,p-1). (n,p) means n choose p

Combinatarics is very useful. One who is dealing with double counting or double counting is very useful. When you are trying to prove some formal such as counting the # of The permutation, the number of your permutations, the number of arrangement, or the number of combinatorics that we can get from a set. We can prove this formulas by using the double counting technique. In fact, we need to have To see how we can do or count as something twice, the same thing, twice in a different manner. That's what we're going to prove in this video. In fact, we have a set Of size n and and we want to choose a subset of size P from that set of size n, So in this case, we say that we have n choose p., that's how we Define the number of subsets Of size p that we can get from n .in our case here, we're going to prove a relation that that relates n and to n minus 1 And we can prove this one using some techniques. Using the fact that we can double counting. So we can count from the right and we can count from the left and we equate them to get the result that we need. This is very helpful when dealing with probability and combinatorics. Combinatorics, In this case can help us a lot By counting the number of elements of subsets we can prove that in many different ways we can probably be using induction. We can prove it using double counting and we can prove it using set Theory, But also we can prove it using a bijection between the number of subset of set a and number of functions that goes from subset a to zero one. This is a nice one. I a nice formula that we can approve later.
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