Question 731622: i have been doing combinations,and i have researched about subsets? and i found out that subsets are 2 to the power n but now i have a question ,given a subset ,how do you find the possible outcomes of choosing a specific number,ie (1,2,3,5,5,6,7,8,9,10,11) ,how many subsets contain the number 5 how many subsets contain exactly three elements, one of which is 3
d. contain exactly five elements, but neither 3 nor
and the question gets complex when it says such,please help
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! The number of subsets with  to  elements from a set with  elements is  elements, there are  subsets.
How many subsets of {1,2,3,4,5,6,7,8,9,10,11} contain the number 5?
One of those subsets will be {5}, with just one element.
If you remove the number 5 from each of the subsets containing 5, you would get all the subsets of {1,2,3,4,6,7,8,9,10,11} and there is  or  of those (counting the empty set and the whole 10-element {1,2,3,4,6,7,8,9,10,11} set
That is the number of subsets containing 5, counting {5} and {1,2,3,4,5,6,7,8,9,10,11}.
How many subsets of {1,2,3,4,5,6,7,8,9,10,11} contain exactly three elements, one of which is 3?
Removing 3 from each of those subsets would give you all the subsets of {1,2,4,5,6,7,8,9,10,11} with exactly 2 elements and that is  subsets. There are several different combination symbols for that and you know which one you are expected to use.
How many subsets of {1,2,3,4,5,6,7,8,9,10,11} have 5 elements but contain neither 3 not 5?
All of those subsets can be made from {1,2,4,6,7,8,9,10,11} and there is
 of them.
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