SOLUTION: Let A = {1, 2, 3, 4, 5, 6}. (a) How many subsets of 4 elements does the set A have? (b) How many subsets of A have no more than 3 elements?

Algebra ->  Subset -> SOLUTION: Let A = {1, 2, 3, 4, 5, 6}. (a) How many subsets of 4 elements does the set A have? (b) How many subsets of A have no more than 3 elements?       Log On


   

Question 998322: Let A = {1, 2, 3, 4, 5, 6}.
(a) How many subsets of 4 elements does the set A have?

(b) How many subsets of A have no more than 3 elements?
Answer by ikleyn(52798) About Me  (Show Source):
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Let A = {1, 2, 3, 4, 5, 6}.
(a) How many subsets of 4 elements does the set A have?
(b) How many subsets of A have no more than 3 elements?
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a) C%5B6%5D%5E4 = %286%2A5%29%2F%281%2A2%29 = 30%2F2 = 15.

b) C%5B6%5D%5E1 + C%5B6%5D%5E2 + C%5B6%5D%5E3 = 6 + 15 + 20 = 41.

Or  42,  if to add the empty subset.

Do you know what  C%5Bn%5D%5Em  is?

If not,  look into the lesson  Introduction to Combinations  in this site.