The number of triangles that can be formed by 5 points in a line and 3 points on a parralel line is __


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Question Number 180520 by cortano1 last updated on 13/Nov/22

$The number of triangles$ $that can be formed by 5 points$ $in a line and 3 points on a parralel line$ $is___$
	Answered by nikif99 last updated on 13/Nov/22

	$C o m b i n e a n y t w o p o i n t s o f t h e b o t t o m$ $l i n e w i t h e a c h p o i n t o f t h e t o p l i n e$ $a n d v v .$ $C_{2}^{5} \times 3 + C_{2}^{3} \times 5 = 30 + 15 = 45$
	Commented by cortano1 last updated on 13/Nov/22

	$my way = (\begin{matrix} 8 \\ 3 \end{matrix}) - (\begin{matrix} 5 \\ 3 \end{matrix}) - (\begin{matrix} 3 \\ 3 \end{matrix})$ $= 56 - 10 - 1 = 45$
	Answered by Acem last updated on 13/Nov/22

	${N u m}_{T r .} = C_{1}^{5} C_{2}^{3} + C_{2}^{5} C_{1}^{3} = 45$ $T h e m e t h o d a b o v e i s m o r e c o m p r e h e n s i b l e$
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