permutation and combination

[匿名]

2012-08-27 8:00 pm

Why the calculation of
a) how many ways can 7 ppl be arranged on 4 seats
and
b) how many ways can 4 ppl be arranged on 7 seats
are the same?

I don't want just the calculation process,
but EXPLANATION.
it is also the question 18 c) in Rev.ex 9 in 'Mathematics in Action 5B'

THANK YOU:DDDD

回答 (1)

fooks

2012-08-27 8:57 pm

✔ 最佳答案

Case I : 7 people are arranged on 4 seats.

Firstly, 4 people are selected from the 7 people. Number of ways
= C(7,4)
= 7!/4!3!

Then the 4 selected people take the 4 seats. Number of ways
= P(4,4)
= 4!

Number of ways that 7 people are arranged on 4 seat
= (7!/4!3!) * 4!
= 7!/3!
= P(7,4)

Case II : 4 people are arranged on 7 seats.

Firstly, 4 seats are selected from the 7 seats. Number of ways
= C(7,4)
= 7!/4!3!

Then the 4 people take the 4 selected seats. Number of ways
= P(4,4)
= 4!

Number of ways that 4 people are arranged on 7 seats
= (7!/4!3!) * 4!
= 7!/3!
= P(7,4)

Compare Cases I and II :

Number of ways that 7 people are arranged on 4seat
= Number of ways that 4 people are arranged on 7 seats

參考: fooks

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