📘 Quiz

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Question 1 / 2
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1
In how many ways can 8 items be distributed into 4 distinct groups, allowing for any number of items per group?
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Solution: Step 1: Understand that each item can be placed in any of the 4 groups. Step 2: For each item, there are 4 possible groups to place it in. Step 3: Since there are 8 items, and each has 4 options for placement, the total number of ways = 4^8. Step 4: This is because each item's placement is independent of the others, leading to multiplication of possibilities.
2
A candidate must answer 5 questions from 2 sections, each with 5 questions. How many ways can the candidate select questions if at least 2 questions are from each section?
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Solution: Step 1: Identify the conditions: at least 2 questions from each section Step 2: Break into cases: (3 from section 1 and 2 from section 2) or (2 from section 1 and 3 from section 2) Step 3: Calculate combinations for each case: (5C3 * 5C2) + (5C2 * 5C3) Step 4: Evaluate combinations: 5C3 = 10, 5C2 = 10 Step 5: Calculate: (10 * 10) + (10 * 10) = 100 + 100 = 200
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