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JEE MATHEMATICS MCQ: PERMUTATIONS

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Analyzing +4 | -1
Find the number of permutations x1,x2,x3,x4,x5x_{1}, x_{2}, x_{3}, x_{4}, x_{5} of numbers 1,2,3,4,51,2,3,4,5 such that the sum of five products x1x2x3+x2x3x4+x3x4x5+x4x5x1+x5x1x2x_{1} x_{2} x_{3}+x_{2} x_{3} x_{4}+x_{3} x_{4} x_{5}+x_{4} x_{5} x_{1}+x_{5} x_{1} x_{2} is divisible by 3
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Correct option: B
80
The correct answer is 80 because the sum of the products is divisible by 3 if x2+x4x_2 + x_4 is divisible by 3, leading to 8 combinations for x2x_2 and x4x_4, and then 10 permutations for the remaining numbers.

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