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Your math club has 20 members. In how many ways can it select a president, a vice-president, and a treasurer if no member can hold more than one office?

Guest Feb 21, 2015

Best Answer 

 #1
avatar+81077 
+10

We have 20 ways to pick the president.

And, after he/she is chosen, 19 ways to pick the vice-president.

And then, 18 ways to pick a treasurer.

So  20 x 19 x 18 = 6840 different ways

We could also find this answer by using a permutaion  .... P(20,3)  = 6840  .... OR ....by counting sets

C(20,3) = 1140 possible sets of 3 different people.....but.....each set can be arranged in 3! = 6 ways.

So  ...  1140 x 6  =  6840

I always like this last one best......we have two tasks .... 1) pick all of the possible different sets, 2) arrange each of these in all possible ways.....

 

CPhill  Feb 21, 2015
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2+0 Answers

 #1
avatar+81077 
+10
Best Answer

We have 20 ways to pick the president.

And, after he/she is chosen, 19 ways to pick the vice-president.

And then, 18 ways to pick a treasurer.

So  20 x 19 x 18 = 6840 different ways

We could also find this answer by using a permutaion  .... P(20,3)  = 6840  .... OR ....by counting sets

C(20,3) = 1140 possible sets of 3 different people.....but.....each set can be arranged in 3! = 6 ways.

So  ...  1140 x 6  =  6840

I always like this last one best......we have two tasks .... 1) pick all of the possible different sets, 2) arrange each of these in all possible ways.....

 

CPhill  Feb 21, 2015
 #2
avatar+91491 
0

Well Chris, you have given lots of choices there  LOL    :))

Melody  Feb 22, 2015

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