In how many ways can 6 boys and 2 girls be seated in 8 chairs if the two girls can not be seated next to each other.
A) 40313
B) 40312
C) 35280
D) 5040
E) 720
The way I approached this problem:
Total number of ways in which both boys and girls can be seated = 8! = 40320
Total number of ways in which two girls can sit next to each other = 7!2! = 10080
Total number of ways in which two girls can NOT sit next to each other = 40320 - 10080 = 30240
Can someone help me find out what I am doing wrong here as I don't see 30240 as one of the answer choices?
Permutation: girls not sitting together
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- arora007
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C is actually ( 8! - 7! ) , they might have forgotten about the 2! ways in which the two girls can sit besides eachother...
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Your approach is sound. To cut down on the arithmetic, you should hold off multiplying until the final calculation:sevenplus wrote:In how many ways can 6 boys and 2 girls be seated in 8 chairs if the two girls can not be seated next to each other.
A) 40313
B) 40312
C) 35280
D) 5040
E) 720
The way I approached this problem:
Total number of ways in which both boys and girls can be seated = 8! = 40320
Total number of ways in which two girls can sit next to each other = 7!2! = 10080
Total number of ways in which two girls can NOT sit next to each other = 40320 - 10080 = 30240
Can someone help me find out what I am doing wrong here as I don't see 30240 as one of the answer choices?
8! - (7! * 2) = 7! (8 - 2) = 7! * 6 = 5040 * 6 = 30240.
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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].
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