Permutations & Combinations
Combinations from Identical Objects
Grade 11
Question:
<p>How many selections of atleast one red ball can be made from a bag containing 4 red balls and 5 black balls, where balls of the same colour are identical?</p>
Step-by-Step Solution
Key Concept: For identical objects, selections depend on choosing 0 to n objects. Use the multiplication principle for independent groups of identical objects.
<p><strong>Step 1:</strong> Number of selections of atleast one red ball from 4 identical red balls = 4</p><p><strong>Step 2:</strong> Number of selections of any number of black balls from 5 identical black balls = 5 + 1 = 6</p><p><strong>Step 3:</strong> Required number of selections = 4 × 6 = 24</p><p>∴ Answer is 24.</p>
Correct Answer: 24