HMMT 十一月 2011 · GEN 赛 · 第 3 题

HMMT November 2011 — GEN Round — Problem 3

[ 4 ] Alberto, Bernardo, and Carlos are collectively listening to three different songs. Each is simultane- ously listening to exactly two songs, and each song is being listened to by exactly two people. In how many ways can this occur?

解析

[ 4 ] Alberto, Bernardo, and Carlos are collectively listening to three different songs. Each is simultane- ously listening to exactly two songs, and each song is being listened to by exactly two people. In how many ways can this occur? ( ) 3 Answer: 6 We have = 3 choices for the songs that Alberto is listening to. Then, Bernardo and 2 Carlos must both be listening to the third song. Thus, there are 2 choices for the song that Bernardo 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