Permutations & Combinations
Derangements
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 both her coat and her hat.</p>
<p>(A) 2048</p>
<p>(B) 1936</p>
<p>(C) 1956</p>
<p>(D) 1978</p>
Step-by-Step Solution
Key Concept: Use inclusion-exclusion principle to count derangements where no woman receives both her original coat and hat together.
<p>Not provided in the text.</p>
Correct Answer: C