Question 233437: 16) In how many ways can 7 people be chosen and arranged in a straight line, if there are 9 people from whom to choose? 16) ______
A) 72 ways B) 63 ways
C) 144 ways D) 181,440 ways
*****AM I USING PERMUTATION, COMBINATIONS or is it 9*7=63?******
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! If where in the line they are placed is important, then you are dealing with permutations.
If where in the line they are placed is not important, then you are dealing with combinations.
Example:
choose 2 out of 3 people.
people are abc.
If order is important, then you can choose ...
ab
ac
bc
ba
ca
cb
= 6 ways
If order is not important, then you can choose ...
ab
ac
bc
= 3 ways
If permutations, the answer would be n! / (n-x)! where n is the total number to choose from and x is the amount you want to draw from that population.
n = 3, x = 2, permutations = 3! / 1! = 3*2*1/1 = 6
If combinations, the answer would be n! / ((n-x)! * x!)
n = 3, x = 2, combinations = 3! / (1! * 2!) = 3*2*1/1*2*1 = 3
In your problem, the numbers come out as follows:
Permutations = 9! / (9-7)! = 9! / 2! = 9*7*6*5*4*3*2*1/2*1 = 181440.
Combinations = 9! / (2!*7!) = 9*8*7! /2!*7! = 9*8/2*1 = 72/2 = 36
Since 36 is not one of the answers, I would assume permutations and select D.
If it was just combination, they would have said:
16) In how many ways can 7 people be chosen if there are 9 people from whom to choose?
The question was posede as:
16) In how many ways can 7 people be chosen and arranged in a straight line, if there are 9 people from whom to choose?
The word arranged should have been your permutation clue.
That's what I think, anyway.
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