1。
Consider a set with n elements, how many subsets (power set) does it have?
There is one way to calculate it. Each element has two choices, so that the total number of subsets will be 2^n
Another way, the cardinality of any subset must be >=0 and
sum C(n, k)
2.
Consider polynomial (x+y)^n, expanding it
we have (x+y)^n = sum C(n, k) x^k y^{n-k}
set x = 1, y = 1
There are many ways more to prove it..
有很多办法
所有跟帖:
•
or you can simply count it, if your teacher does not
-idiot94-
♂
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01/29/2009 postreply
06:20:54