Quiz 11
Discrete Mathematics · 2 problems · solutions hidden, click to reveal
Flashcards
Problems
A group has 7 men and 3 women.
(a) How many committees have exactly 2 men and 2 women?
(b) How many ways can the group stand in a line so that no two women are adjacent?
(a) How many committees have exactly 2 men and 2 women?
(b) How many ways can the group stand in a line so that no two women are adjacent?
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(a) \(\binom{7}{2}\binom{3}{2} = 21 \cdot 3 = 63\).
(b) Arrange the 7 men (\(7!\)); they create 8 gaps. Place the 3 women in distinct gaps, ordered: \(\dfrac{8!}{5!}\). Total: \(7! \cdot \dfrac{8!}{5!}\).
(b) Arrange the 7 men (\(7!\)); they create 8 gaps. Place the 3 women in distinct gaps, ordered: \(\dfrac{8!}{5!}\). Total: \(7! \cdot \dfrac{8!}{5!}\).
Find the next three larger permutations in lexicographic order after \(4173652\).
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Answer: \(4175236,\ 4175263,\ 4175326\).
\(4173652 \to 4175236 \to 4175263 \to 4175326.\)