Question

2. A standard deck consists of 52 cards, Cards are divided into four suits: hearts , diamonds clubs & and spades. Each suit is further divided into 13 ranks:1, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, and K. Cards with rank J, Q, or K are known as face cards, How many different 5-card hands can you draw that contain: (a) Exactly three face cards? (b) At least two hearts cards? (c) Two cards of one rank and three cards of a different rank? Special instructions: in order to receive full credit, justify your numerical answers by explaining how you set up the computation. For example, you should indicate if you are using such tools as the addition or multiplication principles, permutations, combinations, or other counting techniques 1. Ali, Blake, Charlie, and Dallas walk into a movie theater. The theater is completely ful except for one row of 15 seats. In how many ways can they: (a) Select four seats without occupying them? (b) Arrange themselves in four seats? (c) Select four consecutive seats without occupying them? (d) Arrange themselves in four consecutive seats? Now assume the seats are numbered from 1 to 15, and that seat number 7 is already occupied. In how many ways can they: (e) Arrange themselves in four seats all on the same side of seat number 7? (f) Arrange themselves in four seats so that Ali and Blake are on one side of seat number 7 while Charlie and Dallas are on the opposite side? while the other two are on the opposite side?

Answer 1

hos esacty 3 foce cosds r-e sreed select 3 face oss fsom cice othes 12 Totel ce Selected in aus 4 was ニ1123×4c Different 5-cad hands 2oaso (子1600

usi handhos at least oo hast Caods Thus tord hast CaoS-13 and ether cands つ1+ ha-aho, at least tuoheest Cascls」 he t-e band Can Contain 2 3 4)S The selection selectlon( 13, メーと 30 3 13 3 3 39 t Sco hans f at least twoHeastss 13 乂31 | 952940

K ars tce Casdsofadt fent Too CaoCG sank Selecta danks This is due cx ' need to sen This is done in 13 3 Nombes o lesen 5 casi honds 1.3 | 267G96