In my textbook MP is strictly reserved to counting lists. Does what I do below to count subsets work?Consider 3 men(Ace, Bob, Corry) and 3 women(Ann, Beth, Candace). Suppose we need to choose a team with 2 men and 2 women in it. An example team is { Ace, Ann, Beth, Bob } which is the union of { Ace, Bob } { Beth, Ann } . So we simply count 2−lists whose first element is a set of two men and whose second element is a set of two women. We get the same number of 2−lists if their first element is a set of two women. There are ( 3 2 ) = 8 two-men subsets and that many two-women subsets. So there are 8 choices for the first element and 8 choices for the second one. In all there are 8 2 = ( 3 2 ) 2 = 64 two element lists = teams with two men and two women in each.

Question

In my textbook MP is strictly reserved to counting lists. Does what I do below to count subsets work?Consider 3 men(Ace, Bob, Corry) and 3 women(Ann, Beth, Candace). Suppose we need to choose a team with 2 men and 2 women in it. An example team is   {  Ace, Ann, Beth, Bob  } which is the union of   {  Ace, Bob  }  {  Beth, Ann  }  . So we simply count 2−lists whose first element is a set of two men and whose second element is a set of two women. We get the same number of 2−lists if their first element is a set of two women. There are                               (                            3        2                              )                      =  8 two-men subsets and that many two-women subsets. So there are 8 choices for the first element and 8 choices for the second one. In all there are       8    2    =                                          (                                    3          2                                      )                                2    =  64 two element lists = teams with two men and two women in each.

Marlee Guerra · Accepted Answer

it&#039;s all good except                     (                    3      2                      )              =  3 (not 8) so the true answer should be 9.