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Question Number 180585 by mr W last updated on 14/Nov/22

t h e r e a r e 5 p o i n t s o n a l i n e a n d 4

p o i n t s o n a p a r a l l e l l i n e .

h o w m a n y q u a d r i l a t e r a l s c a n b e

f o r m e d w i t h t h e s e p o i n t s a s

v e r t r i c e s ?

Answered by nikif99 last updated on 14/Nov/22

A n y t w o p o i n t s o u t o f 5 i n t h e 1 s t

l i n e = C_{2}^{5} = 10 c o m b i n e d w i t h a n y t w o

p o i n t s o u t o f 4 i n t h e 2 n d l i n e =

C_{2}^{4} = 6 m a k e a t o t a l o f 60 .

Commented by mr W last updated on 14/Nov/22

w i t h 4 p o i n t s w e c a n f o r m 3 d i f f e r e n t

q u a d r i l a t e r s, n o t o n l y o n e .

Commented by nikif99 last updated on 14/Nov/22

I f I w e l l u n d e r s t o o d y o u r c o m m e n t S i r,

y o u m e a n t h e r e a r e 3 p o s s i b l e

q u a d r i l a t e r s h a v i n g 2 v e r t i c e s i n

a n y 4 p o i n t s o f a l i n e ?

Commented by nikif99 last updated on 14/Nov/22

Commented by mr W last updated on 14/Nov/22

i m e a n : w h e n w e h a v e 4 p o i n t s, w e c a n

f o r m 3 d i f f e r e n t q u a d r i l a t e r a l s,

s e e e x a m p l e b e l o w .

s o t a t a l l y 60 \times 3 = 180 q u a d r i l a t e r a l s

c a n b e f o r m e d .

Commented by mr W last updated on 14/Nov/22

Commented by nikif99 last updated on 14/Nov/22

P E R F E C T . I s e e . Y o u a r e r i g h t, S i r .

Answered by cortano1 last updated on 14/Nov/22

(\begin{matrix} 9 \\ 4 \end{matrix}) - (\begin{matrix} 5 \\ 4 \end{matrix}) - (\begin{matrix} 4 \\ 4 \end{matrix})

= \frac{9.8.7.6}{4.3.2.1} - 5 - 1

= 126 - 6 = 120

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