HMMT 十一月 2011 · GEN 赛 · 第 3 题

英文解析

3. [ 4 ] Alberto, Bernardo, and Carlos are collectively listening to three different songs. Each is simultaneously listening to exactly two songs, and each song is being listened to by exactly two people. In howmany ways can this occur?
   ( )
   Answer: 6 We have = 3 choices for the songs that Alberto is listening to. Then, Bernardo and 3
   Carlos must both be listening to the third song. Thus, there are 2 choices for the song that Bernardo 2
   shares with Alberto. From here, we see that the songs that everyone is listening to are forced. Thus,
   there are a total of 3 × 2 = 6 ways for the three to be listening to songs.
   General Test