# Questionbank: Permutation and Probability

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Clue - FInd the number of rearrangements and then focus on the number of digits

## Sum of Rearrangements

Q.28: Of 22 points on a plane, 8 are on a straight line, 7 are on another straight line and 10 are on a third straight line. How many triangles can be drawn by connecting some two points from these 22?
1. 22C3
2. 22C3 - (8C3+ 7C3 +10C3)
3. 22C3 + (8C3+ 7C3 +10C3)
4. 8C3+ 7C3 +10C3

Choice B. 22C3 - (8C3+ 7C3 +10C3)

## Detailed Solution

From the 22 points on a plane we can form 22C3 triangles but it is given that 8 are on one straight line, 7 are on another straight line and 10 more are on another straight line, so we can form triangles on joining points which are on straight lines so we have to subtract (8C3+ 7C3 +10C3) from the total.

Hence, we can form 22C3 - (8C3+ 7C3 +10C3) triangles.

Correct Answer : 22C3 - (8C3+ 7C3 +10C3)

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