There are 12 Cantonese songs, 8 Mandarin songs and 5 English songs stored in the MP3 player of Katherine. If 6 songs are selected to play, how many playing sequences are there in each of the following cases?
(a) Selecting 2 songs from each language.
(b) At least 1 English song is selected.
Permutaions&combinations2
2010-12-20 5:01 am
回答 (2)
2010-12-20 5:17 am
✔ 最佳答案
a) First of all, the total no. of possible combinations is 12C2 x 8C2 x 5C2 = 18480For each combination, there are 6! = 720 possible sequences.
Hence total no. of possible sequences = 18480 x 720 = 13305600
b) When no English song is selected, no. of possible sequences = 13P6
So for the condition that at least 1 English song is selected, no. of possible sequences = 14P6 - 13P6 = 926640
2010-12-19 21:20:05 補充：
Corr. to (b):
When no English song is selected, no. of possible sequences = 20P6
So for the condition that at least 1 English song is selected, no. of possible sequences = 25P6 - 20P6 = 99604800
參考: 原創答案
2010-12-20 5:10 am
(a) (12C2)(8C2)(5C2)=18480
(b).(35C6)-(20C6)=1584400
(b).(35C6)-(20C6)=1584400
收錄日期: 2021-04-13 17:42:47
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20101219000051KK01153