Discrete math - probability

In the Republic of Frestonia, citizens play a card game called Qallin. They do use the usual cards we do in other card games. Here are the rules of Quallin: . Each card has a rank from 1 to 20 and an accent (similar to the suit), which is one .A hand is SIX cards (as opposed to the FIVE of poker) A Quallin happens when all of the cards in your hand are primes. For example, the following hand is a Quallin: { 21. 2A. 312. 512. 7, 11 } Note that it's completely ok to have two or even three same primes, but of different accents! A Super Qual in is a Quallin where all of the primes are of the same accent. For example, the following hand has a Super Quallin: {21. 31. 71. 131. 171. 191.} A Run is when you have the six cards in order. As in the game of poker, we do NOT allow wrap-arounds! For example, the following is a run: {2. 3A. 412. 512. 6. 7A } But the following is NOT a run: {20. 1A. 212. 3. 4. 5A). In Qualiin. unlike in poker. there is NO "Ace" card to play the role of both the high and low end of runs, as Aces do with straights in poker. So the rank 1 can only be used as the low end, and the rank 20 can only be used as the high end . A Super Run is a Run where all the cards are of the same accent. It is sim- ilar to the straight flush in poker. For example, the following is a Super Run: Fill in the table below. Leave your results in terms of factorials, products of factorials, ( notation, etc. You must show your work in the space provided to S notation, etc. You must show your provided to you below and on the opposite page Hand Super Quallin Quallin that is not a Super Quallin Super Rurn un that is not a Super Ruin Probability SHOW YOUR WORK BELOW