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22 Feb 2022, 06:45
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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A photo is going to be taken of 8 people arranged in two rows. Three people will be in the first row and 5 people will be in the second row. Two of the people in the photo are Sabah and George. If each position in the photo is randomly assigned, which of the following is equal to the probability that Sabah is in the leftmost position in the first row, and George is somewhere on the back row?
A. \(\frac{3*5*6!}{8!}\)
B. \(\frac{5*6!}{8!}\)
C. \(\frac{2*6!}{8!}\)
D. \(\frac{2!}{6!}\)
E. \(\frac{5*4!}{6!}\)
Are You Up For the Challenge: 700 Level Questions
A. \(\frac{3*5*6!}{8!}\)
B. \(\frac{5*6!}{8!}\)
C. \(\frac{2*6!}{8!}\)
D. \(\frac{2!}{6!}\)
E. \(\frac{5*4!}{6!}\)
Are You Up For the Challenge: 700 Level Questions
22 Feb 2022, 14:59
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The probability of any given person being in the leftmost front row seat is just
1/8
leaving 2 front row seats and 5 second row seats remaining.
The probability of George being anywhere in that second row is therefore
5/7
So the probability of both of these is
1/8 * 5/7 = 5/56
Examining the answer choices
B. 5*6!/8! = 5/(8*7) = 5/56
Alternatively
Place Sabah in the leftmost front seat:1 choice
Place George in any of the 5 back seats: 5 choices
Arrange the other 6 people 6! ways
Total ways: 1*5*6!
Total ways to seat 8 people: 8!
Probability: 5*6!/8!
Posted from my mobile device
1/8
leaving 2 front row seats and 5 second row seats remaining.
The probability of George being anywhere in that second row is therefore
5/7
So the probability of both of these is
1/8 * 5/7 = 5/56
Examining the answer choices
B. 5*6!/8! = 5/(8*7) = 5/56
Alternatively
Place Sabah in the leftmost front seat:1 choice
Place George in any of the 5 back seats: 5 choices
Arrange the other 6 people 6! ways
Total ways: 1*5*6!
Total ways to seat 8 people: 8!
Probability: 5*6!/8!
Posted from my mobile device
General Discussion
23 Feb 2022, 01:00
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Probability of choosing Sarah in the leftmost position = 1C1 / 8C1=> 1/8;
Probability of choosing any two people other than George for 1st row sitting is = 6C2 / 7C2 => 5/7
Therefore, the combined probability is = 1/8 * 5/7
Hence, IMO option B is the answer
Probability of choosing any two people other than George for 1st row sitting is = 6C2 / 7C2 => 5/7
Therefore, the combined probability is = 1/8 * 5/7
Hence, IMO option B is the answer
