A haiku is a poem with three lines: the first line contains 5 syllables, the second line 7 syllables, and the last line 5 syllables. If each word in each list shown is used at most once, how many different haiku can be made with these words?
2-syllabes: unknown, measure, counting, logic, number, system, fourteen, rhombus
3-syllabes: algebra, triangle, reasoning, calculus, difference, separate, remainder
Hint 1: Don't think about the words as words. Just remember that there are 8 2-syllable words and 7 3-syllable words, and they are all unique. Make sure to correct for overcounting with this information!
Hint 2: The first and last lines can only have one 2-syllable and one 3-syllable. The second line can have two 2-syllables, and one 3-syllable. Use this to your advantage.