If the exclusion of Miss Jones and Mr Smith serving together was not present, the are 15C4 = 1365 ways of selecting the committee. Miss Jones can serve on the committee in the following ways: a) with 3 men b) with 2 men and another woman c) with 1 man and 2 other women d) with 3 other women. Arrangement d) obviously presents no restrictions. Arrangement a) has 7C3 ways excluding Mr Smith, and 8C3 ways if Mr Smith was included. Arrangement b) has 7C2 * 6 ways excluding Mr Smith, and 8C2 * 6 ways if Mr Smith was included. Arrangement c) has 7 * 6C2 ways excluding Mr Smith, and 8 * 6C2 ways if Mr smith was included. The reductions in ways caused by the restriction are as follows: a) 8C3 - 7C3 = 21 ways b) 6(8C2 - 7C2) = 42 ways c) 6C2 = 15 ways The total reduction in the number of ways is: 21 + 42 + 15 = 78. Therefore the total number of ways of selecting the committee, while observing the restriction, is 1365 - 78 = 1287 ways.
