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$3.00 counting principles; probability 8-37

• From Mathematics: Probability , Mathematics: Combinatorics
• Closed, but you can still post tutorials
• Due on May. 17, 2009
• Asked on May 14, 2009 at 1:20:50PM

Q:

In this exercise we study the connection between sets and combinations.
a. Given a set with n elements, what is the number of subsets of size 0? of size 1? of size 2? of size n?
b. Using your answer from part a, give an expression for the total number of subsets of a set with n elements.
c. Using your answer from part b and a result from Chapter 7, explain why the following equation must be true:
(n) + (n) + (n) + ... + (n) = 2(to the n power)
(0) (1) (2) (2)

d. verify the equation in part c for n=4 and n=5

ANSWERS:
a. (n), or 1; (n), or n; (n); (n), or 1
(0) (1) (2) (n)

b. (n)+(n)+(n)+ ... +(n)
(0) (1) (2) (n)

 

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