Step 1: Understanding the Concept:
When a specific item or person must always be included in a selection, that person's place is fixed. This effectively reduces both the total number of items to choose from and the number of spots remaining to be filled.
Step 2: Key Formula or Approach:
If 1 particular person is always included, the number of ways to choose $r$ people from $n$ is:
\[ ^{n-1}C_{r-1} \]
Step 3: Detailed Explanation:
1. Total number of persons ($n$) = 10.
2. Selection size ($r$) = 4.
3. Since 1 particular person is always included, we have already picked 1 person.
4. Remaining persons to choose from = $10 - 1 = 9$.
5. Remaining spots to fill = $4 - 1 = 3$.
6. Number of ways = $^9C_3$.
\[ ^9C_3 = \frac{9 \times 8 \times 7}{3 \times 2 \times 1} \]
\[ = 3 \times 4 \times 7 = 84. \]
Step 4: Final Answer:
The number of ways to make the selection is 84.