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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

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by BTGmoderatorDC » Fri Feb 19, 2021 6:13 pm

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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. [3×5×6!][/8!]
B. [5x6!][/8!]
C. [2x6!][/8!]
D. [2!][/6!]
E. [5x4!][/6!]


OA B

Source: Magoosh
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Re: 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 wi

by deloitte247 » Thu Feb 25, 2021 6:18 am
Total no of ways of arranging 8 people $$=8!$$
There is only one way to arrange sabah that is in is in the leftmost position in first row
George is somewhere in the backrow and there are 5 places there, so
number of ways to arrange George
$$=5C_1=\frac{5!}{1!\left(5-1\right)!}=\frac{5!}{1\cdot4!}=5$$
Removing George and Sabah, Total number of people left = (8-2)=6 and they can be arranged in 6! ways in which Sabah can be placed in the leftmost position and also with George somewhere in the back row $$=5\cdot6!$$ $$\Pr obabaility=\frac{5\cdot6!}{8!}$$ $$Answer\ is\ Option\ B$$
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