SOLUTION: Kindly answer this question please!!! Thanks!!!! A commander pilot and an assistant for a flight to Mars are chosen from 15 astronauts. In how many

Algebra ->  Permutations -> SOLUTION: Kindly answer this question please!!! Thanks!!!! A commander pilot and an assistant for a flight to Mars are chosen from 15 astronauts. In how many      Log On


   

Question 217304: Kindly answer this question please!!! Thanks!!!! A commander pilot and an assistant for a flight to Mars are chosen from 15 astronauts. In how many ways can the two men be chosen for the 2 positions?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
The answer is %2815%21%29+%2F+%28%282%21%29%2A%2813%21%29%29+=+%2815%2A14%29%2F%281%2A2%29+=+105
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To make it easier to show, assume it was 5 candidates for 2 positions.
The formula would then be %285%21%29+%2F+%28%282%21%29%2A%283%21%29%29+=+%285%2A4%29%2F%282%2A1%29+=+10
Let the 5 candidates be abcde
Then the possible ways they could be chosen would be:
ab
ac
ad
ae
bc
bd
be
cd
ce
de
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Same concept applies with larger numbers.
Your answer is 105 different ways.
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The general formula for x positions chosen out of n candidates is:
%28n%21%29%2F%28%28n-x%29%21%2A%28x%29%21%29
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