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Condition for Two Lines to Be Parallel

The number of...

Question

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

^{8} C_{3}

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^{8} C_{3} -^{5} C_{3}

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45

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None of these

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Solution

The correct option is A $45$
$N u m b e r o f w a y s o f s e l e c t i n g 3 p o i n t s o u t o f 8 p o i n t s =^{8} C_{3} = b u t n o t a l l t h e s e l e c t e d g r o u p o f 3 p o i n t s w i l l r e s u l t i n t o a t r i a n g l e . I f w e s e l e c t a n y 3 p o i n t f r o m t h e g i v e n 5 p o i n t s i n o n e l i n e t h e n n o t r i a n g l e w i l l b e f o r m e d =^{5} C_{3} S i m i l a r l y w e c a n s e l e c t 3 p o i n t s f r o m t h e 3 p o i n t s g i v e n i n o n e l i n e b u t i t w i l l n o t r e s u l t i n t o a t r i a n g l e = 1 ∴ n u m b e r o f t r i a n g l e s f o r m e d =^{8} C_{3} -^{5} C_{3} - 1 = 56 - 10 - 1 = 45$

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