A) \[^{m+n+k}{{C}_{3}}\]
B) \[^{m+n+k}{{C}_{3}}{{-}^{m}}{{C}_{3}}{{-}^{n}}{{C}_{3}}-{{}^{k}}{{C}_{3}}\]
C) \[^{m}{{C}_{3}}{{+}^{n}}{{C}_{3}}{{+}^{k}}{{C}_{3}}\]
D) None of these
Correct Answer: B
Solution :
Total number of points are\[m+n+k\], the \[\Delta 's\] formed by these points \[{{=}^{m+n+k}}{{C}_{3}}\] Joining 3 points on the same line gives no triangle, such \[\Delta 's\] are \[^{m}{{C}_{3}}{{+}^{n}}{{C}_{3}}{{+}^{k}}{{C}_{3}}\] Required number\[{{=}^{m+n+k}}{{C}_{3}}{{-}^{m}}{{C}_{3}}{{-}^{n}}{{C}_{3}}{{-}^{k}}{{C}_{3}}\].
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