F.5 maths combination HELP!!!!

2014-12-17 5:04 am

There are 10 points in a plane,no three of which are collinear except for 4 that are all in a straight line.How many straight lines can be formed by joining pairs of the points?
Ans:40 , WHY????

A woman has 12 friends and wishes to invite 6 of them to a party.Find number of ways she may do this if
(b) two of the friends is a couple and will not attend separately
Ans:420 , WHY???
(c)two of the friends are not speaking and will not attend together
Ans:714 , WHY???

Miss Kwong wants to recruit 8 students from a class of 22 students to join growth camp.Find the number of ways to recruit the students if
(a) two of the students are best friends and they will not join the camp separately
Ans:=2C2(20C6)+20C8
=164730 , WHY???
(b) there is conflict between two of the students and they cannot join the camp together
Ans: =281010 , WHY???

更新1:

其實第一題問咩@@

回答 (1)

50418129

2014-12-17 4:46 pm

✔ 最佳答案

1.

firstly 'straight line' and 'line segment' are different.
there are totally 10C2 ways to form straight lines.
among them, there are 4C2 straight lines are the same.
so, there are 10C2 - 4C2 + 1 ways to form different straight lines.

2.

(b)
case i, the couple will attend, there are 2C2 x 10C4 = 210 ways
case i, the couple will not attend, there are 10C6 = 210 ways
so, totally there are 210 + 210 ways.

(c)
if two friends will both attend, there are 2C2 x 10C4 = 210 ways
so, they will not both attend, there are 12C6 - 210 ways.

3.

same as question 2

參考: knowledge

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