Permutations and Combinations
Gap Method
Premium Question
Grade 11
Question:
The number of ways to arrange $5$ identical red and $4$ identical blue balls in a row such that no two blue balls are adjacent is:
(1) $6$
(2) $15$
(3) $10$
(4) $20$
Step-by-Step Solution
Key Concept: Place 5 red balls creating 6 gaps ( $\_R\_R\_R\_R\_R\_$ ). Choose 4 of the 6 gaps for blue balls: $\binom{6}{4} = 15$ (balls are identical so no ordering within colour).
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)