Counting techniques, pigeonhole, recurrences and elementary graph theory.
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Q1 · Combinatorics · HARD
How many ways can we arrange the letters of the word EQUATION so that no two vowels are adjacent?
Q2 · Combinatorics · EASY
In how many ways can 5 identical red balls and 3 identical blue balls be arranged in a row?
Q3 · Combinatorics · MEDIUM
In how many ways can 5 boys and 4 girls be arranged in a row such that no two girls sit together?
Q4 · Combinatorics · HARD
How many 4-digit numbers can be formed using digits 1, 2, 3, 4, 5, 6 (without repetition) such that the number is divisible by 4?
Q5 · Combinatorics · MEDIUM
In how many ways can the letters of the word OLYMPIAD be arranged such that the vowels O, I, A occupy even positions?