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Three rooks are placed on the $5 \times 5$ board shown so that no two are in the same row or column. In how many ways can this be done?

Competition practicePermutations & Combinations

A600
B100
C60
D2300

Step-by-Step Solution

Choose 3 rows:

^{5} C_{3} = 10

; choose 3 columns: 10; match rows to columns:

3! = 6.10 \times 10 \times 6 = 600. (2300 =^{25} C_{3}

ignores the rule.)

Answer: A) 600

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