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Ana Ben Cora Dina Elphie and Francis are to select a chairperson secretary and a treasurer.in how many ways can they choose if Elphie must hold one of the position?
Wiki User
∙ 15y ago
They need three positions - let's call them C, S and T Let's put Elphie into position C Then there are 5 people left to choose from for position S, and when that position is filled there are 4 people left to choose from for position T 5 x 4 = 20 Now as we con't care what position Elphie is given that means that there are 3 ways to allocate the jobs making sure that Elphie has one of them 3 x 20 = 60 If we use C, S and T we can draw up a table with the possibilities ... C S T # E A B # E A C # E A D # E A F # E B A # E B C # E B D # E B F # E C A # E C B # E C D # E C F # E D A # E D B # E D C # E D F # E F A # E F B # E F C # E F D # A E B # A E C # A E D # A E F # B E A # B E C # B E D # B E F # C E A # C E B # C E D # C E F # D E A # D E B # D E C # D E F # F E A # F E B # F E C # F E D # A B E # A C E # A D E # A F E # B A E # B C E # B D E # B F E # C A E # C B E # C D E # C F E # D A E # D B E # D C E # D F E # F A E # F B E # F C E # F D E Now, you might think that 1, 5, 21, 25, 41 and 45 are all the same as they just contain the same three people, A B and E - but as they are in different positions the 'choice' is different each time. A, B and E are one 'combination', but the different ways that they can fill the positions are six 'permutations'.
Wiki User
∙ 15y ago
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