1. The table below shows teh categories of movies shown last month.
Local movie (I) = 1
Local movie (IIA) = 2
Local movie (IIB) = 3
Local movie (III) = 1
Foreign movie (I) = 3
Foreign movie (IIA) = 6
Foreign movie (IIB) = 5
Foreign movie (III) = 2
(a) How many arrangements are there to select 1 local movie and 1 foreign movie?
Both (7C1 x 16C1) and (7P1 x 16P1) can get the answer = 112 . But which one is more suitable? Why?
(b) How many arrangements are there to select 4 movies in different categories?
(c) How many arrangements are there to select 3 movies in different categories?
2. 10 males and 13 females have applied for a job. The manager, Mr. Ma, plans to interview 5 males and 5 females. Assume that one candidate will be interviewed each time, how many sequences of interviews can be arranged? (express in SCI notation and corr. to 3 s.f.)
Answer:
1 (a) 112
1 (b) 768
1 (c) 640
2 1.18 x 10^12
thank you for your help
please show steps.
nPr / nCr (5 marks)
2010-11-29 3:05 am
回答 (1)
2010-11-29 4:02 am
✔ 最佳答案
(1) (a) 7C1 x 16C1 is suitable since we do not care the order of the selection(b) Cat I = 4; Cat 2A = 8; Cat2B = 8; Cat3 = 3Number of ways = 4 x 8 x 8 x 3 = 768(c) Number of ways = 4 x 8 x 8 + 4 x 8 x 3 + 4 x 8 x 3 + 8 x 8 x 3 = 640(2) Number of ways to choose the males = 10C5 = 252Number of ways to choose the females = 13C5 = 1287Consider the orders, the number of possible sequence = 252 x 1287 x 10!= 1.177 x 10^12
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