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##### :) Mathistillfun

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Permutations and Combinations Question. Pls help thanks!!

Date Posted: 4 weeks ago
Views: 17
AC Lim
4 weeks ago
:) Mathistillfun
4 weeks ago
Is it okay if I could have working the question (combinatorics and permutations method)

Thanks!!
:) Mathistillfun
4 weeks ago
My answer is 50 :(
J
4 weeks ago
90
AC Lim
4 weeks ago
Do you use nPr and nCr to find the answer?
AC Lim
4 weeks ago
89. Manual count. :) not nPr or nCr ;(
J
4 weeks ago
I tried both permutation and combination, and manual counting.

Counted from one side of the triangle at a time to avoid double counting. Tried from each of the 3 sides and got 90 for all
:) Mathistillfun
4 weeks ago
Wow. Can you show me the combinatorics and permutations method
:) Mathistillfun
4 weeks ago
Thanks so much
J
4 weeks ago
Case ① : △base is either the bottom horizontal line, or a line from the right vertex of the big △ to its left side.

We choose the left side and base of the △ first. There are 6 possible lines to choose from.

Number of ways to choose 2 lines to make the left side and the base = 6C2 = 15

Now we need the right side to form the △. There are 4 lines that extend from the left vertex of the big △ to its right side, for us to use.

Number of ways to choose a right side
= 4 (or 4C1 which = 4 anyway)

Total number of triangles here
= 15 x 4
= 60

Case ② : base is a line from the left vertex of the big △ to its right side.

We choose the right side and base of the△ first. There are 5 possible lines to choose from. We cannot consider the bottom horizontal line as it has been used in case ①. It would result in double counting if we did.

Number of ways to choose 2 lines to make the right side and the base = 5C2 = 10

Now we need the left side to form the △. There are 3 lines that extend from the right vertex of the big △ to its left side, for us to use.

Number of ways to choose a right side
= 3 (or 3C1 which = 3 anyway)

Total number of triangles here
= 10 x 3
= 30

Total triangles = 60 + 30 = 90
J
4 weeks ago
Done editing. This is only one way to get the answer. There's a few others.

Not easy at all. It would be hard for A level students, and to think they give it you all at Sec 1..

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