How many more ways can 10 juniors running for the positions of president, vice president, secretary, treasurer be selected when compared to 12 sophomores running for 5 identical positions of class representative's?

Question

Mathematics

Sydney Sutton

16 January, 17:34

How many more ways can 10 juniors running for the positions of president, vice president, secretary, treasurer be selected when compared to 12 sophomores running for 5 identical positions of class representative's?

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Answers (1)

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Azaria Bryant · Answer 1

10 juniors are running for 4 positions.

There are ten people who can get into the first spot

Nine people for the second

8 people for the third

7 for the fourth

10x9x8x7 = 5040 different ways.

For the sophomores: 12x11x10x9x8 = 95040

However, the positions are identical which means that the order doesn't matter. (There's a difference between A getting postion 1, B for 2, C for 3, D for 4 and B for 1, A for 2, C for 3, D for 4)

There are 5 identical positions, therefore we divide this by 5! (5x4x3x2x1) = 120

95040/120 = 792

Juniors have 5040 positions, sophomores have 792