SOLUTION: consider the set A={a,b,c,d,e,f,g,h}. find the number of subsets of A which contain atleast 6 elements and include 'c' and 'e'.

Algebra ->  Permutations -> SOLUTION: consider the set A={a,b,c,d,e,f,g,h}. find the number of subsets of A which contain atleast 6 elements and include 'c' and 'e'.      Log On


   

Question 892685: consider the set A={a,b,c,d,e,f,g,h}. find the number of subsets of A which contain atleast 6 elements and include 'c' and 'e'.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Case 1:  {c,e,_,_,_,_}

Choose 4 letters to go in the 4 blanks from the 6 letters
{a,b,d,f,g,h}.  That C(6,4) = 15 ways.

Case 2:  {c,e,_,_,_,_._}

Choose 5 letters to go in the 5 blanks from the 6 letters
{a,b,d,f,g,h}.  That C(6,5) = 6 ways.

Case 3:  {c,e,a,b,d,f,g,h}, (the whole set).

That's 1 way.

Answer 15+6+1 = 22 ways

Edwin