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A seven-person committee composed of Adam, Betty, Cameron, David, Edward, Fritz, and Grace is to select a chairperson, secretary, and treasurer
A seven-person committee composed of Adam, Betty, Cameron, David, Edward, Fritz, and Grace is to select a chairperson, secretary, and treasurer. How many selections are there where Betty is the chairperson, and Adam and Edward are not officers?
12
20
24
210
None of the above
3. A seven-person committee composed of Adam, Betty, Cameron, David, Edward, Fritz, and Grace is to select a chairperson, secretary, and treasurer. How many selections are there where Adam, Cameron and Grace are not officers?
210
None of the above
12
20
24
4. A standard deck of cards contains 52 cards. The cards are evenly divided into four suits (spades, clubs, diamonds, and hearts) with 13 cards in each suit (A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K). Find the number of (unordered) five-card poker hands that contain a full house (three of a kind and a pair).
624
3,744
7,488
44,928
None of the above
Expert Solution
2. Answer: 12
The rest 4 should have 2 officers and 2 non-officers. There are C(4,2)=6 choices.
For the two officers, they can exchange their positions. Thus totally there are
6*2=12 choices.
3. Answer: 24
For the rest 4, there are 3 officers and one non-officer. There are C(4,3)=4 choices.
For the three officers, we have a permutation for positions. there are 3!=6 permutations.
Therefore, totally 4*6=24 choices.
4. Answer: 3744
For the three of a kind, there are 13 choices of kinds from A,K,Q,J,10,9,8,7,6,5,4,3,2.
For each kind, there are C(4,3)=4 choices. For the rest pair, there are 12 kinds,
for each kind, there are C(4,2)=6 choices.
Therefore, totally 13*4*12*6=3744
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