This is counting discrete Math. Please kindly answer all questions. Thank you so much.

\fSection 5 [2n pts]: More Counting A standard Zcard deck of playing cards has 13 ranks [Ace,'2,3,4__5__6,7_.8.9_.1\"Jackueening] and 4 suits per rank (Hearts 5'. Clubs '. Dianmnds O. Spades Q). 1. How many di'erent ve-card hands are there? 2. How many ve-card hands Domains exactly 2 Aces and 2 eights {of any suit). The cards may an . in an order. One possible hand is shown below. 3. A card dealer deals two cards: one at a time from a standard 52-card deck. [u how many ways can the rst card dealt be a RED card {Diamonds or Hearts of any rank} foliowed by .3. QUEEN {of any suit] as the second card? Section 6: Even More Counting [t is October when thoughts turn to baseball and the Red Sox winning the 'Worid Series! (Maybe next year.) 1. The world series is played by the nal two teams not. eliminated in the piayofs. The team that wins the torrid series is the rst team to win 4 games. As soon as one team or the other has Iwon 4 games, the series is over and no more games are played. Explain why the world series can not go more than 1' games. 1ithat mathematical principle are you appealing to in your answer? 2. If the Red Sm: play in the World Series, in. how main}r ways can they win the \"Form Series? Each way is dened be a sequence of \"fins {W] or Losses (L). Possible winning sequences inelnde \""WWVE, \"FLEM'LW. and LLL'NVHRM'. Remember that the 1World Series can go at most 7 games: and no more games are piayed after one of the two teams wins 4 games. For foil credit. state your answer in the form of a concise mathematical expression and then mince you answer to a single integer. {No credit is given for simply enumerating all possibilities.) 3. On a basebali team there are .9 player positions. designated 1-9. The manager decides the batting order of the nine players. This is sometimes called the batting lineup or simply the iineap. How many lineups have the li inelders {1.2.3.4. 5.6} batting together {in an}.r order} and the 3 outelder's {T2819} batting together in any order. One possible batting sequence isSbT:-9::-l+63-2arpdandanotherisFiriIipAiblyar 8 r \"r". A concise mathematical expression sniees for an answer but be sun-e to explain your