Computer Sciences > GATE 2023 > Discrete Mathematics
Let U = {1, 2,...,n}, where n is a large positive integer greater than 1000. Let k be a positive integer less than n. Let A, B be subsets of U with |A| = |B| = k and A ∩ B = ∅. We say that a permutation of U separates A from B if one of the following is true.
- All members of A appear in the permutation before any of the members of B.
- All members of B appear in the permutation before any of the members of A.
How many permutations of U separate A from B?
A
n!
B
n
2k (n - 2k)!
C
n
2k (n - 2k)!
(k!)2
D
2 n
2k (n - 2k)! (k!)2

Correct : d

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Related Topics

permutations set theory combinatorics GATE Computer Sciences 2023 GATE CS 2023 Q51 separating subsets permutations counting permutations discrete mathematics GATE

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