SOLUTION: A bag contains 12 balls numbered from 1 to 12. Two balls are selected from the bag at the same time Let event E=the two numbers differ by 4 How many outcomes are in the comp

Here is the complete sample space S.  It contains 12C2 = 12*11/2 = 66 elements,
called 'outcomes'. 

S = { {1,2}, {1,3}, {1,4}, {1,5}, {1,6}, {1,7}, {1,8}, {1,9}, {1,10}, {1,11}, {1,12},
{2,3}, {2,4}, {2,5}, {2,6}, {2,7}, {2,8}, {2,9}, {2,10}, {2,11}, {2,12}, {3,4}, 
{3,5}, {3,6}, {3,7}, {3,8}, {3,9}, {3,10}, {3,11}, {3,12}, {4,5}, {4,6}, {4,7},
{4,8}, {4,9}, {4,10}, {4,11}, {4,12}, {5,6}, {5,7}, {5,8}, {5,9}, {5,10}, {5,11}, 
{5,12}, {6,7}, {6,8}, {6,9}, {6,10}, {6,11}, {6,12}, {7,8}, {7,9}, {7,10}, {7,11}, 
{7,12}, {8,9}, {8,10}, {8,11}, {8,12}, {9,10}, {9,11}, {9,12}, {10,11}, {10,12}, {11,12} }

Here is the event E (subset of the above sample space) such that the two
numbers in each outcome differ by 4. It contains 8 outcomes:

E = { {1,5}, {2,6}, {3,7}, {4,8}, {5,9}, {6,10}, {7,11}, {8,12} }

The complement of E consists of all the outcomes of S other than the
ones in E.

Therefore the complement of E contains 66 - 8 = 58 outcomes. Here is E',
or EC.

E' = EC = { {1,2}, {1,3}, {1,4}, {1,6}, {1,7}, {1,8}, {1,9}, {1,10}, {1,11}, {1,12},
{2,3}, {2,4}, {2,5}, {2,7}, {2,8}, {2,9}, {2,10}, {2,11}, {2,12},
{3,4}, {3,5}, {3,6}, {3,8}, {3,9}, {3,10}, {3,11}, {3,12},
{4,5}, {4,6}, {4,7}, {4,9}, {4,10}, {4,11}, {4,12}, 
{5,6}, {5,7}, {5,8}, {5,10}, {5,11}, {5,12}, 
{6,7}, {6,8}, {6,9}, {6,11}, {6,12}, 
{7,8}, {7,9}, {7,10}, {7,12}, 
{8,9}, {8,10}, {8,11},
{9,10}, {9,11}, {9,12},
{10,11}, {10,12}, {11,12} }

Answer: 58 outcomes

Edwin