| (a) |
Explain, with examples, how to distinguish between situations that involve permutations and those that involve combinations. |
| (b) |
Develop, generalize, explain, and apply strategies for determining the number of ways that a subset of $k$ can be selected from a set of $n$ different elements. |
| (c) |
Develop, generalize, explain, and apply strategies to determine combinations of $n$ different elements taken $r$ at a time in situational questions. |
| (d) |
Explain why $n$ must be greater than or equal to $r$ in the notation $ _nC_r $ or $ (\table n; r) $. |
| (e) |
Prove or explain using examples $_nC_r = _n C _(n-r)$ or $(\table n; r) = (\table n; n-r)$. |
| (f) |
Solve equations involving combinations e.g. $_nC_2=15$ or $(\table n; 2)=15$. |
| (g) |
Explore and describe patterns found within Pascal's triangle, including the relationship between consecutive rows. |
| (h) |
Explore and describe the relationship between the coefficients of the terms in $(x+y)^n$, and the combinations. |
| (i) |
Develop, generalize, explain, and apply strategies for expanding $(x+y)^n,n≤4$. |
| (j) |
Develop, generalize, explain, and apply strategies for determining specific terms within a particular expansion of $(x+y)^n$ given $n∈\ℕ$. |
