How many ways are there to place circles in an 8 x 8 grid so that each row has exactly one circle and each column has exactly one circle? Here is an example of one such way: A 8 C 1 2 3 4 5 6 7 8 O O O

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 46SE: How many ways can a committee of 3 freshmen and 4 juniors be formed from a group of 8 freshmen and...
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How many ways are there to place circles in an 8 x 8 grid so that each row has
exactly one circle and each column has exactly one circle?
Here is an example of one such way:
ABC OF CH
D
E
1 2
FO
G
O
0
0
6
O
088
6 7 0
O
0
o
08x7x6x5x4 x 3 x 2 x 1
064²
O648 - (8x7x6×5×4×3×2×1)
0648
08+7+6+5+4+3+2+1
064-(8+7+6+5+4+3+2+1)
None of the other choices listed here is correct.
08²
Transcribed Image Text:How many ways are there to place circles in an 8 x 8 grid so that each row has exactly one circle and each column has exactly one circle? Here is an example of one such way: ABC OF CH D E 1 2 FO G O 0 0 6 O 088 6 7 0 O 0 o 08x7x6x5x4 x 3 x 2 x 1 064² O648 - (8x7x6×5×4×3×2×1) 0648 08+7+6+5+4+3+2+1 064-(8+7+6+5+4+3+2+1) None of the other choices listed here is correct. 08²
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