Permutations & Combinations
Distributing People into Cars
nta_pyq_2023_apr
Grade 11
Question:
8 persons transported in 3 cars (at most 3 each). Number of ways is
Step-by-Step Solution
Key Concept: Distribute 8 into groups of 3,3,2 (only valid distribution): $\frac{\binom{8}{3}\binom{5}{3}\binom{2}{2}}{...}$ since cars are distinct.
$\binom{8}{3}\binom{5}{3}\times3=1680$.
Correct Answer: 3