Permutations & Combinations Tutorial

Direct Formula Application

Use the standard Permutations & Combinations formula directly when the question gives all inputs.

When to Use: Use this when all required values are explicitly given and no reverse logic is needed.

Step-by-Step Method

1. Identify the exact quantity asked (result, rate, value, distance, etc.).
2. Map given values to the formula variables.
3. Substitute carefully and simplify one operation at a time.
4. Cross-check unit consistency and compare with options.

Worked Example

Question: Find 25% of 640.

1. Percentage means per 100, so 25% = 25/100.
2. Compute: (25/100) x 640.
3. First divide 640 by 100 = 6.4.
4. Then multiply 6.4 x 25 = 160.

Final Answer: 160

Option Analysis

• If options include 64 or 80, those come from wrong percentage operations.
• 160 is exactly one-fourth of 640, which confirms correctness.

Common Mistakes

• Using percentage as whole number without dividing by 100.
• Rounding too early and losing accuracy.
• Mixing up increase/decrease questions with direct percentage questions.

Quick Shortcut: 25% = one-fourth, 50% = half, 10% = divide by 10. Use these mental anchors first.

Generated 15 focused questions for this pattern.