How many ways could three people sit at a table with five seats in which two of the five seats will remain empty?
A) 8
B) 12
C) 60
D) 118
E) 120
The OA is C.
Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.
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How many ways could three people...
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GMATGuruNY
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Let the 3 people be A, B and C.swerve wrote:How many ways could three people sit at a table with five seats in which two of the five seats will remain empty?
A) 8
B) 12
C) 60
D) 118
E) 120
Number of options for A = 5. (Any of the 5 seats.)
Number of options for B = 4. (Any of the 4 remaining seats.)
Number of options for C = 3. (Any of the 3 remaining seats.)
To combine these options, we multiply:
5*4*3 = 60.
The correct answer is C.
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Out of 5 positions, 1 to 5, the 2 empty chairs can be arranged, for example, at positions 1 and 2, written as 12 below.
Using this notation, here is a list of the empty seat positions: 12,13,14,15,23,24,25,34,35,45 = 10 combinations.
That answer is not provided in the question.
Using this notation, here is a list of the empty seat positions: 12,13,14,15,23,24,25,34,35,45 = 10 combinations.
That answer is not provided in the question.
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GMATGuruNY
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The result in blue must be multiplied by the number of ways the 3 people can be arranged in the occupied seats (3!):DrMaths wrote:Out of 5 positions, 1 to 5, the 2 empty chairs can be arranged, for example, at positions 1 and 2, written as 12 below.
Using this notation, here is a list of the empty seat positions: 12,13,14,15,23,24,25,34,35,45 = 10 combinations.
That answer is not provided in the question.
10 * 3! = 60.
We could also proceed as follows:
From the 5 seats, the number of ways to choose 3 to be occupied = 5C3 = (5*4*3)/(3*2*1) = 10.
Within the occupied seats, the number of ways to arrange the 3 people = 3! = 6.
To combine the options above, we multiply:
10*6 = 60.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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