There are 10 true-false questions in an examination. In how many distinct ways can these questions b

Question

There are 10 true-false questions in an examination. In how many distinct ways can these questions be answered?

Accepted Answer

{"type":"doc","content":[{"content":[{"marks":[{"type":"bold"}],"text":"Step 1 (Identify choices per question):","type":"text"},{"text":" For each of the 10 true-false questions, there are exactly 2 possible answers (either True or False).","type":"text"}],"type":"paragraph"},{"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step 2 (Apply product rule):"},{"text":" Since the answer choice for each question is independent, we multiply the choices:","type":"text"}],"type":"paragraph"},{"attrs":{"latex":"\text{Total ways} = 2 \times 2 \times \dots \times 2 = 2^{10}"},"type":"math_block"},{"attrs":{"latex":"2^{10} = 1024"},"type":"math_block"},{"type":"paragraph","content":[{"marks":[{"type":"bold"}],"text":"Step 3 (Conclusion):","type":"text"},{"type":"text","text":" The questions can be answered in 1024 distinct ways, which corresponds to option index "},{"type":"text","marks":[{"type":"code"}],"text":"3"},{"type":"text","text":" in "},{"marks":[{"type":"code"}],"text":"['20', '100', '512', '1024']","type":"text"},{"type":"text","text":"."}]}]}

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Guide / Hint

Solution