Permutations & Combinations
Distribution of Objects
Grade 11
Question:
<p>Number of ways in which 12 different things can be divided among five persons so that they can get 2, 2, 2, 3, 3 things respectively, is</p>
<p>(a) \(\frac{12!}{(3!)^2(2!)^3}\)</p>
<p>(b) \(\frac{12! \cdot 5!}{(3!)^2(2!)^3}\)</p>
<p>(c) \(\frac{12!}{(3!)^2(2!)^4}\)</p>
<p>(d) \(\frac{12! \cdot 5!}{(3!)^2(2!)^4}\)</p>
Step-by-Step Solution
Key Concept: When dividing among distinct persons with specified group sizes, do not divide by factorial of number of persons.
<p>Since the persons are distinct (they get specific distributions), we do not divide by 5!. We simply partition 12 things into groups of sizes 2, 2, 2, 3, 3 and assign them to the 5 persons in order. The answer is $\frac{12!}{(3!)^2(2!)^3}$.</p>
Correct Answer: A