Question

۱۲) با نقاط موجود در شکل زیر چند مثلث می توان رسم کرد؟

Explanation:

⚡ Using what you learned: Distinguishing Between Permutations and Combinations

Step 1: Count the points

Count the total number of points on the circle in the given image:
There are \( 6 \) distinct points on the circle.

Step 2: Determine the combination formula

To form a triangle, we need to choose any \( 3 \) points from the \( 6 \) available points. Since the order in which we select the vertices of a triangle does not matter, we use combinations:

$$ \binom{n}{r} = \frac{n!}{r!(n-r)!} $$

where \( n = 6 \) and \( r = 3 \).

Step 3: Calculate the number of triangles

Substitute the values into the combination formula:

$$ \binom{6}{3} = \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = 20 $$

Answer:

\( 20 \) triangles can be drawn.