more improved notes

reading/000_Introduction to Probability, Statistics, and Random Processes/ch2/notes.ipynb

@@ -63,6 +63,56 @@
     "\n",
     "- **unordered sampling with replacement:** $\\binom{n + k - 1}{k}$"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2e93e0fe",
+   "metadata": {},
+   "source": [
+    "## Problem Solving Principles"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "87279e59",
+   "metadata": {},
+   "source": [
+    "When solving a combinatorics problem, consider:\n",
+    "1. Does order matter?\n",
+    "    - Yes → Permutations\n",
+    "    - No → Combinations\n",
+    "\n",
+    "    - \"Are HHHTT and THHHT the same outcome to me?\"\n",
+    "\n",
+    "2. Are we sampling with of without replacement?\n",
+    "    - Without replacement → Hypergeometric (phone problem)\n",
+    "    - With replacement → Binomial (coin flips)\n",
+    "    \n",
+    "    \"Can the same item be chosen twice?\"\n",
+    "3. Are the \"groups\" labeled or unlabeled?\n",
+    "    - Labeled/distinguishable → Just multiply combinations\n",
+    "    - Unlabeled/interchangeable → Divide by k!\n",
+    "\n",
+    "    \"Does it matter which group is called group 1?\"\n",
+    "4. Are the items distinguishable?\n",
+    "    - Distinguishable → Each item is unique, classical probability applies\n",
+    "    - Indistinguishable → Outcomes are not equally likely, be careful\n",
+    "\n",
+    "      \"Could I label these items 1 to n?\"\n",
+    "5. Is complement of inclusion-exclusion easier?\n",
+    "    - Complement → When \"at least\" or \"at most\" language appears\n",
+    "    - Inclusion-Exclusion → When events overlap\n",
+    "\n",
+    "    \"Is the opposite event simpler to count?\"\n",
+    "6. Am I counting each outcome exactly once? \n",
+    "  - If yes, done. Otherwhise we are overcounting or undercounting"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9c5783dc",
+   "metadata": {},
+   "source": []
   }
  ],
  "metadata": {