SOLUTION: A computer is printing out subsets of a 5 element set (possibly including the empty set). a. at least how many sets must be printed to be sure of having at least 4 identical subse

Question 357242: A computer is printing out subsets of a 5 element set (possibly including the empty set).
a. at least how many sets must be printed to be sure of having at least 4 identical subsets on the list?
b. at least how many identical subsets are printed if there are 161 subsets on the list?
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Answer by sudhanshu_kmr(1152) (Show Source): You can put this solution on YOUR website!

Total no. of possible subsets of 5 elements (including empty set)
= 5C0 + 5C1 + 5C2 + 5C3 +5C4 + 5C5 = 1 + 5 +10 + 10 + 5 + 1 = 32

a). no. of subset to ensure at least 4 identical subsets = 32*3 + 1

= 97

b). 161 = 32 * 5 + 1

so, at least 6 identical subsets are printed.

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