In the game of 5-card draw poker using a standard deck of 52playing cards, it is often counter-intuitive that drawing astraight (i.e. five cards of sequential rank) is more likely tooccur than drawing a flush (i.e. five cards of the same suit).However, this is something that we can confirm withmathematics!

(a) How many different ways could we get a straight fromrandomly drawing five cards? Explain how this number is computedusing combinations. (Note: you may include straight flushes in thiscount.)

(b) How many different ways could we get a flush from randomlydrawing five cards? Explain how this number is computed usingcombinations. (Note: you may still include straight flushes.)

(c) Find the probabilities of drawing a straight and drawing aflush. Which one is more likely to occur?

(d) Now suppose you want to invent a new game similar to pokerwhich has players draw FOUR cards instead of five. So now astraight is four cards of sequential rank and a flush is four cardsof the same suit. Repeat the previous three problems for this newgame.