Question

i need help! please help

How many lines are determined by 7 points, no 3 of which are collinear? How may triangles are determined by the same points if no 4 are coplanar?

Answer 1

A line is defined by 2 points

Answer 2

So if you had 7 points, labeled A through G, then some lines may be

AB
AC
EF
AG

etc

Answer 3

does that help?

Answer 4

its going to be a combination so is it going to be 7C2 ?

Answer 5

yep, you nailed it

Answer 6

order doesn't matter since AB = BA

Answer 7

line AB = line BA

Answer 8

Okay i get the first sentence but how about the second sentence.

Answer 9

we still have these 7 points

A, B, C, D, E, F, G

Answer 10

but now we're forming triangles, so some triangles that may form are

ABC
ABD
EFG
CDF

etc

Answer 11

so its going to be 7C3 ?

Answer 12

yep

Answer 13

some teachers want you to leave it as 7C2, but you might have to evaluate that

Answer 14

same for 7C3

Answer 15

OKAY one last question so when i get the answers of 7C2 and 7C3 do i multiply them or do i leave them seperate

Answer 16

they're separate since they are answers to separate questions

Answer 17

well they're not totally separate since they still use the same 7 points, but you know what I mean

Answer 18

so 7c2=21 and 7c3=35
so 21 X 35 =735 ?

Answer 19

21 and 35 are the two answers, but you don't multiply them

Answer 20

there are 21 distinct lines given 7 points (no three are collinear)

there are 35 distinct triangles given 7 points (no four are coplanar)

Answer 21

okay i understand

Answer 22

alright great