From the letters in MAGOOSH, we are going to make three-letter "words." Any set of three letters counts as a word, and different arrangements of the same three letters (such as "MAG" and "AGM") count as different words. How many different three-letter words can be made from the seven letters in MAGOOSH?
答案是135 给了两类情况,含有两个“O”的15种,一个O的120种。
官方解答:
Let's break this into two cases, to deal with the double letter.
Case I: "words" with two O's
The non-O letter could take any of three spaces in the word:
XOO
OXO
OOX
In any of those scenarios, the X could be replaced by one of five letters: {M, A, G, S, H}. Five letters in three cases: Case I results in 15 "words" with two O's.
Case II: "words" with one O or no O's
Now, we can ignore the second O. We are simply picking 3 letters from the pool: {M,A,G,O,S,H}.