HMMT 二月 2014 · 冲刺赛 · 第 13 题

英文解析

13. [ 8 ] An auditorium has two rows of seats, with 50 seats in each row. 100 indistinguishable people sitin the seats one at a time, subject to the condition that each person, except for the first person to sitin each row, must sit to the left or right of an occupied seat, and no two people can sit in the sameseat. In how many ways can this process occur?
    ( )
    98 49100
    Answer: 2 First, note that there are 2 ways a single row can be filled, because each ofthe 49 people after the first in a row must sit to the left or to the right of the current group of people 50
    in the row, so there are 2 possibilities for each of these 49 people.
    ( )
    49100
    Now, there are ways to choose the order in which people are added to the rows, and 2 ways to
    ( )50
    98100
    fill up each row separately, for a total of 2 ways to fill up the auditorium.
    °50