急 ! F5 排列與組合 ex2

2012-12-04 9:27 am

請詳細步驟教我計以下三條 :
不要網址回答 :

1) The are 40 students in a class, if 7 students are chosen randomly. Find the number of ways if
(a) they are required to queue up as a straight line
(b) they are required to form a group only

2) 3 uniform white balls and 4 uniform blue balls are given. Find the number of ways if 4 balls are taken randomly and arranged in a row.

3) In the word “SHINGWAI”, 3 letters are taken out at the same time, find the total number of ways.

回答 (1)

micatkie

2012-12-04 10:10 am

✔ 最佳答案

1)
(a)
Number of ways
= 40P7
= 40!/33!
= 93963542400

(b)
Number of ways
= 40C7
= 40!/33!7!
= 18643560

=====
2)
Number of ways to arrange 3 white balls and 1 blue ball
= 4P3 / 3!
= 4! / 3!
= 4

Number of ways to arrange 2 white balls and 2 blue balls
= 4P3 / 2!2!
= 4! / 2!2!
= 6

Number of ways to arrange 1 white ball and 3 blue balls
= 4P3 / 3!
= 4! / 3!
= 4

Number of ways to arrange 4 blue balls
= 4P3 / 4!
= 4! / 4!
= 1

Total number of ways
= 4 + 6 + 4 + 1
= 15

=====
3)
The word "SHINGWAI" contains 2 "I" and 6 other differentletters.

Number of ways that the 3 letters include no "I"
= 6C3
= 6! / 3!3!
= 20

Number of ways that the 3 letters include 1 "I"
= 6C2 x 2C1 / 2
= (6!/4!2!) x (2!/1!1!) / 2
= 15 x 2 / 2
= 15

Number of ways that the 3 letters include 2 "I"
= 6C1 x 2C2
= (6!/5!1!) x (2!/0!2!)
= 6 x 1
= 6

Total number of ways
= 20 + 15 + 6
= 41

參考: micatkie

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