Permutations & Combinations
Distribution of Objects
Grade 11
Question:
<p>Number of ways in which 12 different books can be distributed equally among 3 persons, is</p>
<p>(a) \(\frac{12!}{(4!)^3}\)</p>
<p>(b) \(\frac{12!}{(3!)^4}\)</p>
<p>(c) \(\frac{12!}{(4!)^4}\)</p>
<p>(d) \(\frac{12!}{(3!)^3}\)</p>
Step-by-Step Solution
Key Concept: When distributing n distinct objects equally among k distinct persons, divide n! by the product of factorials of group sizes.
<p>Equal distribution among 3 persons means each gets 4 books. The number of ways is $\frac{12!}{(4!)^3}$ because we divide 12 books into 3 groups of 4, and the order of groups matters (distinct persons).</p>
Correct Answer: A