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Permutations and Combinations Question. Pls help thanks!!
Date Posted: 4 years ago
Views: 429
My answer:48
Is it okay if I could have working the question (combinatorics and permutations method)
Thanks!!
Thanks!!
My answer is 50 :(
90
Do you use nPr and nCr to find the answer?
89. Manual count. :) not nPr or nCr ;(
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
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
Wow. Can you show me the combinatorics and permutations method
Thanks so much
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
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
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..
Not easy at all. It would be hard for A level students, and to think they give it you all at Sec 1..
See 1 Answer
done
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ans:30
I hope this will help you
I hope this will help you
Date Posted:
4 years ago
Question asks for number of triangles. You've missed out some triangles, and also included 4 sided figures in your counting.
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