SOLUTION: 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 w
Algebra.Com
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.
RELATED QUESTIONS
In how many ways can 5 people be chosen and arranged in a straight line, if there are... (answered by richwmiller)
In how many ways can 4 people be chosen and arranged in a straight line, if there are 12... (answered by addingup)
In how many ways can 4 people be chosen and arranged in a straight line, if there are 12... (answered by ikleyn)
If there are 11 people from whom to choose, then how many ways can 4 people could be... (answered by stanbon)
In how many ways can 5 people be chosen and arranged in a straight line, if there are 11... (answered by Alan3354)
A class consists of 12 boys and 15 girls. How many different committees of four can be... (answered by ikleyn)
Ten people (5 men and 5 women) are attending a dinner party. In how many ways can they be (answered by CPhill)
There are seven man and five women in a line at a salsa dance club. the bouncer can't... (answered by ewatrrr)
Hello, I just need someone to check my answers for these questions. Thank You.
1. In... (answered by ikleyn)