Permutations & Combinations
Derangements with Multiple Objects
Grade 11
Question:
<p>Each of 5 women who attend a banquet checks her coat and hat with the receptionist on arrival. Upon leaving, each woman is given a coat and a hat at random. Find the number of ways these coats and hats may be distributed such that nobody gets back either her coat or her hat.</p>
<p>(A) 14400</p>
<p>(B) 118000</p>
<p>(C) 11842</p>
<p>(D) 11844</p>
Step-by-Step Solution
Key Concept: Use inclusion-exclusion to count distributions where no woman receives either her coat or her hat (complete derangement of both objects).
<p>Not provided in the text.</p>
Correct Answer: D