# Combination

 Question 1
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 $A\cap B=\phi$. 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 $\binom{n}{2k} (n-2k)!$ C $\binom{n}{2k} (n-2k)! (k!)^2$ D $2 \binom{n}{2k} (n-2k)! (k!)^2$
GATE CSE 2023   Discrete Mathematics
Question 1 Explanation:
 Question 2
There are 6 jobs with distinct difficulty levels, and 3 computers with distinct processing speeds. Each job is assigned to a computer such that:

The fastest computer gets the toughest job and the slowest computer gets the easiest job.
Every computer gets at least one job.

The number of ways in which this can be done is ___________.
 A 18 B 36 C 65 D 27
GATE CSE 2021 SET-1   Discrete Mathematics
Question 2 Explanation:

 Question 3
The number of permutations of the characters in LILAC so that no character appears in its original position, if the two L's are indistinguishable, is ______.
 A 120 B 24 C 36 D 12
GATE CSE 2020   Discrete Mathematics
Question 3 Explanation:
 Question 4
The number of integers between 1 and 500 (both inclusive) that are divisible by 3 or 5 or 7 is ______________.
 A 135 B 350 C 271 D 335
GATE CSE 2017 SET-1   Discrete Mathematics
Question 4 Explanation:
 Question 5
The number of 4 digit numbers having their digits in non-decreasing order (from left to right) constructed by using the digits belonging to the set {1, 2, 3} is____________.
 A 10 B 15 C 18 D 12
GATE CSE 2015 SET-3   Discrete Mathematics
Question 5 Explanation:

There are 5 questions to complete.