06/04/2020 (2011: National Sprint Round, Problem 12)
Q: Elmo is making three-letter "words" using alphabet blocks. Each of the three blocks has a different letters on each of three faces and pictures on the remaining three faces. How many three-letter "words" can Elmo form if none of the blocks have any letter in common?
There are 3 different letters on each of three blocks, so there are 3 ⋅ 3 ⋅ 3 = 27 combinations on how to order them.
Because none of the letters are the same, there are 3P3 = 6, where "P" is "Permutation," ways to order the 3 blocks.
27 ⋅ 6 = 162 ways.
Comments
Post a Comment