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📐 Mathematics  ·  Permutations and Combinations  ·  JEE

The number of lattice paths from (0,0) to (m,n) moving only right or up:

Answer: C(m+n, m).

  • A m+n
  • B C(m+n, m)
  • C m × n
  • D m! + n!

Correct answer: B. C(m+n, m)

Explanation: Each path needs exactly m right-steps (R) and n up-steps (U): total m+n steps. Choose which m of the m+n steps are R: C(m+n, m). Remaining n are automatically U.

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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