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  9. Q137

HPSC HCS 2021 · Question 137 of 177

If n Cx = 126 and n Px = 3024 , find n and x. ​ ​

Permutations & Combinations

  1. A7, 3
  2. B8, 4
  3. C8, 3
  4. D9, 4Correct

Answer: D. 9, 4

Explanation

nCx = nPx/x! gives x! = 24, so x = 4; then n(n-1)(n-2)(n-3) = 3024 = 9×8×7×6, so n = 9.

Source: HPSC HCS (Ex.Br.) Prelims Paper-II (CSAT) held 12-Sep-2021 (prepp.in compilation); answers per official HPSC answer key

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