Question

Find the value of the combination.

How many straight lines can be drawn through 20 points, of which no three lie on any one straight line?

A. 190
B. 380
C. 1,140

Answer 1

190

Explanation:

no three on one one, so max of two

20C2 = 90

Answer 2

Combination formula:


n C r = (n!)/(r!(n-r)!)

20 C 2 = (20!)/(2!*(20-2)!)

20 C 2 = (20!)/(2!*18!)

20 C 2 = (20*19*18!)/(2!*18!)

20 C 2 = (20*19)/(2!)

20 C 2 = (20*19)/(2*1)

20 C 2 = (380)/(2)

20 C 2 = 190

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Or as a simpler alternative

20*19/2 = 380/2 = 190

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Either way, the final answer is choice A) 190