A drawer in a darkened room contains $100$ red socks, $80$ green socks, $60$ blue socks and $40$ black socks.  A youngster selects socks one at a time from the drawer but is unable to see the color of the socks drawn.  What is the smallest number of socks that must be selected to guarantee that the selection contains at least $10$ pairs?  (A pair of socks is two socks of the same color.  No sock may be counted in more than one pair.)

$ \textbf{(A)}\ 21\qquad\textbf{(B)}\ 23\qquad\textbf{(C)}\ 24\qquad\textbf{(D)}\ 30\qquad\textbf{(E)}\ 50$
To solve this problem, we need to determine the smallest number of socks that must be selected to guarantee that the selection contains at least 10 pairs. A pair of socks is defined as two socks of the same color. 

1. **Identify the worst-case scenario**:
   - In the worst-case scenario, we want to avoid forming pairs for as long as possible. This means we should try to pick socks in such a way that we maximize the number of single socks before forming pairs.

2. **Calculate the number of socks needed to form pairs**:
   - We have 4 colors: red, green, blue, and black.
   - To avoid forming pairs, we can pick up to 1 sock of each color without forming any pairs. This gives us 4 socks (one of each color).
   - After picking 4 socks, the next sock we pick will start forming pairs. 

3. **Forming pairs**:
   - To form 10 pairs, we need 20 socks (since each pair consists of 2 socks).
   - However, we need to account for the initial 4 socks that were picked without forming pairs.

4. **Total number of socks**:
   - We need 4 socks to avoid forming any pairs initially.
   - We need 20 additional socks to form 10 pairs.
   - Therefore, the total number of socks needed is \(4 + 20 = 24\).

5. **Verification**:
   - If we pick 24 socks, we are guaranteed to have at least 10 pairs because:
     - The first 4 socks are all different colors.
     - The next 20 socks will form 10 pairs (since each pair requires 2 socks).

Thus, the smallest number of socks that must be selected to guarantee that the selection contains at least 10 pairs is \( \boxed{24} \).