maths nCr and nPr 1

[匿名]

2010-08-11 7:18 am

please help me. I need steps. (solution at the bottom) thank you. 5 marks

1. 10 horizontal lines and 15 vertical lines are intersected. How many rectangles can be formed?

2. (a) In a badminton tournament, any 2 players must play against each other twice. However, a player was quit after playing 4 matches due to injury. If a total of 60 matches were played finally, how many players were there originally?

Solutions:
1. 4 725
2. (a) 9

回答 (1)

石石

2010-08-11 7:42 am

✔ 最佳答案

1.
= 10C2 x 15C2 <-- no. of choices of horizontal lines x no. of choices of vertical lines
= 45*105
= 4725

Explanation:
(1) A number of n distinct vertical lines and m horizontal lines will form nxm intersection points.
(2) Joining intersection points of any 2 distinct vertical lines and 2 distinct horizontal lines will from a rectangle.
(3) Since order need not to be considered, we shall consider combinations.

2.Let n be the original number of players.
(n-1)C2 + 4 = 60 (*)
(n-1)(n-2)/2 + 4 = 60
(n-1)(n-2)/2 = 56
n^2-3n+2=56
n^2-3n-54=0
(n-9)(n+6)=0
n=9 or -6(rej.)
Therefore, there are 9 players originally.

Explanation for (*):
L.H.S.:
(n-1)C2 = matches played after the injured player quit
4 = matches played before the injured player quit
R.H.S.:
60 = total matches played

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