Combinations⑤ Summary and Comprehensive Problems
Summary
- Permutations (order matters): nPr
- Combinations (order does not matter): nCr
- Combinations with repetition: nHr=(n+r−1)Cr
- General term of the binomial theorem: nCk×a^(n-k)×b^k
Comprehensive Practice Problems
- Find the coefficient of x³y² in (2x+y)^5.
- Find the number of nonnegative integer solutions of a+b+c+d=6.
- How many triangles can be formed from 12 points on a plane, with no 3 points collinear?
Answers
- 5C2×2³×1²=10×8=80
- 4H6=9C6=84
- 12C3=220