SOLUTION: A team is being formed that includes 6 different people. There are six different positions on the
teams. How many ways are there to assign the six people to the six positions?
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teams. How many ways are there to assign the six people to the six positions?
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Question 1193209: A team is being formed that includes 6 different people. There are six different positions on the
teams. How many ways are there to assign the six people to the six positions?
From the context, all 6 people are equally qualified to take any of the 6 position.
So, any of the 6 people for the first position;
any of remaining 5 people for the second position;
any of remaining 4 people for the third position,
. . . and so on . . .
giving 6*5*4*3*2*1 6! = 720 different ways. ANSWER
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We start at 6 and count down by 1 until all six slots are full.
For more information, check out the concept dealing with factorials.
A very closely related topic would be permutations.
6 ways to fill slot A
5 ways to fill slot B
4 ways to fill slot C
3 ways to fill slot D
2 ways to fill slot E
1 way to fill slot F
There are 6*5*4*3*2*1 = 720 ways to fill the six positions where order matters.
Order matters because each position or seat is different from one another.
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