there are 80 pieces of red socks, 90 pieces of white socks and 100 pieces of blue socks in the box. if you want to get 5 pairs of socks that is not white colour and 4 pairs of socks that is not blue colour, at least how many piece(s) of sock(s) is/are needed to be drawn.

To solve this problem, we need to determine the minimum number of sock pieces that must be drawn to guarantee obtaining at least five pairs of non-white socks and four pairs of non-blue socks.

1. **Define the Requirements**:
   - We need **5 pairs of non-white socks**. This means we need 5 pairs of red socks since white socks are excluded.
   - We also need **4 pairs of non-blue socks**. This translates to needing 4 pairs of red or white socks (since blue socks are excluded).

2. **Step-by-Step Solution**:
   - Since each pair consists of 2 socks, getting 5 pairs of red socks requires at least \(5 \times 2 = 10\) red socks.
   - To get 4 pairs of non-blue socks, we could get either red or white socks. However, to ensure 4 pairs (8 socks), we need to consider the worst case of drawing extra blue socks.

3. **Worst-Case Scenario**:
   - The worst case involves drawing as many unwanted colors as possible.
   - To satisfy the requirement of non-blue and non-white socks, we would encounter scenarios where we may draw extra white or blue socks.

To proceed further

There are 80 pieces of red socks, 90 pieces of white socks, and 100 pieces of blue socks in the box. If you want to get 5 pairs of socks that are not white and 4 pairs of socks that are not blue, at least how many pieces of socks need to be drawn?

Determine the minimum number of socks needed to be drawn from a set of red, white, and blue socks to guarantee obtaining 5 pairs of non-white socks and 4 pairs of non-blue socks. This combinatorics problem covers worst-case scenario analysis and applies the Pigeonhole Principle. Suitable for students in Grades 10-12.

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