Question:
The number of triangles whose vertices are at the vertices of an octagon but none of whose side happen to come from the sides of the octagon is
The number of triangles whose vertices are at the vertices of an octagon but none of whose side happen to come from the sides of the octagon is
Updated On: Jul 7, 2022
- 24
- 52
- 48
- 16
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Number of all possible triangles
= Number of selections of 3 points from 8 vertices
$=^8C_3=56$
Number of triangle with one side common with octagon $= 8 ? 4 = 32$
(Consider side $A_1A_2$. Since two points $A_3, A_8$ are adjacent, 3rd point should be chosen from remaining 4 points.)
Number of triangles having two sides common with octagon : All such triangles have three consecutive vertices, viz., $A_1A_2A_3, A_2A_3A_4, ..... A_8A_1A_2.$
Number of such triangles $= 8$
$\therefore$ Number of triangles with no side common $= 56 - 32 - 8 = 16.$
Was this answer helpful?
0
0
Top Questions on Permutations
- How many 4-digit numbers can be formed using the digits 1, 2, 3, 4, 5 without repetition such that the number is divisible by 5?
- BITSAT - 2025
- Mathematics
- Permutations
- From the word "CURVE", how many 3-letter words can be formed out of all 2-letter or more combinations (with all distinct letters)? Find probability of getting a 3-letter word.
- AP EAPCET - 2025
- Mathematics
- Permutations
- 5 men and 4 women are seated in a row. If the number of arrangements in which one particular man and one particular woman are together is $ \alpha $, and the number of arrangements in which they are not together is $ \beta $, then $ \frac{\alpha}{\beta} = $
- AP EAPCET - 2025
- Mathematics
- Permutations
- The number of positive integers less than 10000 which contain the digit 5 at least once is
- AP EAPCET - 2025
- Mathematics
- Permutations
- 5-digit numbers are formed by using the digits 0, 1, 2, 3, 5, 7 without repetition and all of them are arranged in ascending order. Then the rank of the number 70513 is:
- AP EAPCET - 2025
- Mathematics
- Permutations
View More Questions
Notes on Permutations
Concepts Used:
Permutations
A permutation is an arrangement of multiple objects in a particular order taken a few or all at a time. The formula for permutation is as follows:
\(^nP_r = \frac{n!}{(n-r)!}\)
nPr = permutation
n = total number of objects
r = number of objects selected
Types of Permutation
- Permutation of n different things where repeating is not allowed
- Permutation of n different things where repeating is allowed
- Permutation of similar kinds or duplicate objects