Question 250032
a. Given a set with n elements, what is the number of subsets 
of size 0?---------nC0 = 1 
of size 1? of------nC1 = n
size 2?------------nC2= (n(n-1))/2 
of size n?---------nCn = 1
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b. Using your answer from part a, give an expression for the total number of subsets of a set with n elements.--------------
Total number of subsets = nC0 + nC1 + nC2 + ... + nCn = 2^n
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c. Using your answer from part b and a result from Chapter 7, explain why the following
equation must be true: nC0 + nC1 + nC2 + ... + nCn = 2^n
Ans: Every element in the set of "n" is either chosen or not
chosen in each subset.  So the number of possible subsets
is 2^n  (a choice with 2 possible outcomes made n times)
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d. Verify the equation in part c for n=4 and n=5
4C0 + 4C1 + 4C2 + 4C3 + 4C4 
= 1 + 4 + 6 + 4 + 1
= 16
= 2^4
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Note: I'll leave n = 5 to you
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e. Explain what the equation in part c tells you about Pascal’s triangle
The sum of the elements in the kth row is 2^(k-1)
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Cheers,
Stan H.
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