Search any question & find its solution
Question:
Answered & Verified by Expert
Let $P_1, P_2, \ldots ., P_{15}$ be 15 points on a circle. The number of distinct triangles formed by points $P_i, P_j, P_k$ such that $i+j+k \neq 15$ is
Options:
Solution:
2315 Upvotes
Verified Answer
The correct answer is:
$443$
Total number of distinct triangles $={ }^{15} C_3$
Now, we have to exclude that cases in which $i+j+k=15$
Total number of cases in which $i+j+k=15$ is 12 .
$\therefore$ Total number of required triangles
$={ }^{15} C_3-12=455-12=443$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.