Permutations & Combinations
Distribution of Objects
Grade 11
Question:
<p>Number of ways in which 12 different things can be distributed in 3 groups, is</p>
<p>(a) \(\frac{12!}{(4!)^3}\)</p>
<p>(b) \(\frac{12!}{3!(4!)^3}\)</p>
<p>(c) \(\frac{12!}{4!(3!)^3}\)</p>
<p>(d) \(\frac{12!}{(3!)^4}\)</p>
Step-by-Step Solution
Key Concept: When groups are indistinguishable, divide by the factorial of the number of groups.
<p>When distributing 12 different things into 3 indistinguishable groups, we divide by 3! to account for the groups being identical. Each group has 4 things. The answer is $\frac{12!}{3!(4!)^3}$.</p>
Correct Answer: B