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📐 Mathematics  ·  Permutations and Combinations  ·  JEE

How many 5-digit palindromes exist? (Form abcba)

Answer: 900.

  • A 900
  • B 810
  • C 9000
  • D 90

Correct answer: A. 900

Explanation: Form abcba: 'a' determines 1st & 5th, 'b' 2nd & 4th, 'c' middle. a ∈ {1–9}: 9 choices; b ∈ {0–9}: 10; c ∈ {0–9}: 10. Total = 9×10×10 = 900.

StartABCBCACAB6 ordered outcomes (permutations); pairing AB/BA etc gives 3 combinations

Counting tree for selecting 2 items from {A, B, C} without repetition: 3 x 2 = 6 ordered arrangements.

Concept context

Counting, arrangements, and selections

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