<p>The total number of selections of at most 4 things from 9 different things is ______.</p>
Step-by-Step Solution
Key Concept: Sum all combinations from selecting 0 to 4 items from 9 items using the formula C(9,0) + C(9,1) + C(9,2) + C(9,3) + C(9,4). The phrase 'at most 4' means we include all cases from 0 up to and including 4.
<p><strong>Step 1:</strong> Interpret 'at most 4 things' means we can select 0, 1, 2, 3, or 4 things from 9 different things.</p><p><strong>Step 2:</strong> Calculate each combination:</p><ul><li>C(9,0) = 1</li><li>C(9,1) = 9</li><li>C(9,2) = 9×8/2! = 36</li><li>C(9,3) = 9×8×7/(3×2×1) = 84</li><li>C(9,4) = 9×8×7×6/(4×3×2×1) = 126</li></ul><p><strong>Step 3:</strong> Add all cases: 1 + 9 + 36 + 84 + 126 = 256</p><p>∴ Answer: <strong>256</strong></p>
Correct Answer: 256