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NDA 2016

Exam: NDA
Year: 2016
Subject: Mathematics
Chapter: Permutation and Combination

NDA 2016 · Mathematics · Permutation and Combination

Out of 15 points in a plane, n points are in the same straight...

Out of 15 points in a plane,

n

points are in the same straight line. 445 triangles can be formed by joining these points. What is the value of

n

?

Options

A $3$
B $4$
C $5$
D $6$

Correct answer

C. $5$

Step-by-step solution

Here,

{ }^{15} C_3-{ }^n C_3=445

\begin{aligned} & \Rightarrow \quad{ }^n C_3=\frac{15!}{3!12!}-445 \\ & \Rightarrow \quad{ }^{\mathrm{n}} \mathrm{C}_3=10 \\ & { }^3 \mathrm{C}_3=1 ;{ }^4 \mathrm{C}_3=4 ;{ }^5 \mathrm{C}_3=10 \\ & \Rightarrow \quad \mathrm{n}=5 \end{aligned}

$$

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