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Prize Distribution Permutations

CMAT 2025 · Quantitative Techniques & Data Interpretation · Medium · Quantitative Techniques

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In how many ways can the following prizes be given away to a class of 30 students, first and second in Mathematics, first and second in Physics, first in Chemistry and first in English?

  1. A.

    30!/4!

  2. B.

    (30)^4 x (29)^4

  3. C.

    (30)^3 - 1

  4. D.

    (30)^4 x (29)^2

Answer

D

Explanation

Ways to award 1st and 2nd in Mathematics = 30×2930 \times 29. Ways to award 1st and 2nd in Physics = 30×2930 \times 29. Ways to award 1st in Chemistry = 3030. Ways to award 1st in English = 3030. Total ways = (30×29)×(30×29)×30×30=(30)4×(29)2(30 \times 29) \times (30 \times 29) \times 30 \times 30 = (30)^4 \times (29)^2.

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