To find the total number of combinations of magazines you can make from the different categories, we can consider each category separately and then multiply the combinations from each category together.
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News Magazines: You have 6 options. The combinations of choosing any number of magazines from these can be calculated by considering that each magazine can either be included or not included in a combination (2 choices for each magazine: included or not). Therefore, for 6 magazines, the combinations are \(2^6 = 64\).
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Fashion Magazines: Similarly, for 3 fashion magazines, the combinations are \(2^3 = 8\).
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Business Magazines: For 9 business magazines, the combinations are \(2^9 = 512\).
Now, to find the total combinations of magazines you can create across all categories, you multiply the combinations from each category:
\[ Total \ combinations = (2^6) \times (2^3) \times (2^9) \]
Now calculating:
\[ Total \ combinations = 64 \times 8 \times 512 \]
Calculating this step-by-step:
- \(64 \times 8 = 512\)
- \(512 \times 512 = 262144\)
Thus, the total number of combinations of magazines you can make is 262144.
Keep in mind that this total includes the option of selecting no magazine at all (the empty set), which is typically also counted in combinatorial calculations.
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