The results of 20 chess games (win, lose, draw) are to be predicted. How many different forecasts can contain exactly 15 correct results?
For a correct forecast with exactly 15 correct results, 5 other must be wrong. For any game to be wrong there exist 2 ways, as in all, there are 3 possible outcome of a game. So we total (3–1)^5 possible combinations for those wrongly predicted games. Hence for any one of the possibly “15-correct” forecast, we have in all 32 predictions with a similar end-effect.Now, how many of those 15-correct forecasts are possible? 20C15 = 20C5 = 15504, i.e. the number of ways to select those 15 games for which the forecast is correct. Hence in all, we have 15504*32 = 496128.
How many combinations are there in 10 football games?
4 to the power 10 (1,048,576) - home win, away win, score draw, no-score draw - is how a lot of bookies operate, or did before internet gambling grew.The reason for this stems from the Pools Panel.Near-infinite if you go into predicting scorelines and goal scorers and goal times.…Don’t try to predict a whole weekendsworth of Premier League matches. If you must, go for 3 or maybe 4
A playoff between the two teams consists of at most five games, and the first team that wins three games. In how many different ways can the playoff occur?
Answer : 20.Consider two teams A and B.For simplicity, I'm assuming A is winning playoff.So, the number of ways for winning A is:-Winning first 3 games →1 way-Winning at the end of 4th game →→ 3C2=3 ways-Winning at the end of 5th game →→ 4C2=6 waysTotal number of matches in which A can win = 1+3+6 = 10 waysSimilarly, total number of matches in which B can win = 10∴ different ways in which playoff can occur = 10 + 10 = 20
A-level further maths question on geometric distribution?
A chess player X plays a series of games against an opponent Y. For each game, the probability that X wins is p, independently of the results of other games. If X plays 4 games against Y, show that the probability that this series of games contains at least 2 consecutive wins by X is p^2(3-2p) Please help...I have struggling with this q...thank u very much
"I Spy Snap" Card Game bought at yard sale - No Directions. Need Directions please!?
I found this on google so I tried to pick you for best answer but it won't let me so I have to wait until 24 hours but I never thought you could get directions on Google so thanks. Here are directions: Deal out all the cards. Players turn up one card, all at the same time. If you see a match among them, be the first to call out the name of the object! The player with the most cards wins.
Calculate all permutations of a round robin competition?
There are 14 teams. Each team plays each team one A team can Win, Draw or Lose 1- How to find the total competitions permutations 2 - How to find the permutations for a specified number e.g. Permutations for round 10, 11, 12 and 13 3 - If a Win = 4, Draw = 2 and Loss = 0 how can I apply a points total to each possible permutation for each round? "I think there is 2187 combinations per round. For each game there are 3 possible combinations, and there are 7 games, see this spreadsheet. As you add games to the round the tables will grow to the right, there does not seem to be duplicates even when you change the W L D to points " Using wins and losses Using Points Two Games - 9 combinations (3 to power 1) Two Games - 9 combinations (3 to power 1) Team Team A B A B L W 0 4 W L 4 0 D D 2 2 Two Games - 9 combinations (3 to power 2) Two Games - 9 combinations (3 to power 2) Team Team A B C D A B C 2 L W L W 0 4 0 4 L W W L 0 4 4 0 L W D D 0 4 2 2 W L L W 4 0 0 4 W L W L 4 0 4 0 W L D D 4 0 2 2 D D L W 2 2 0 4 D D W L 2 2 4 0 D D D D 2 2 2 2 Three Games - 27 combinations (3 to power 3) Three Games - 27 combinations (3 to power 3) Team Team A B C D E F A B C 2 E F L W L W L W 0 4 0 4 0 4 L W L W W L 0 4 0 4 4 0 L W L W D D 0 4 0 4 2 2 L W W L L W 0 4 4 0 0 4 L W W L W L 0 4 4 0 4 0 L W W L D D 0 4 4 0 2 2 L W D D L W 0 4 2 2 0 4 L W D D W L 0 4 2 2 4 0 L W D D D D 0 4 2 2 2 2 W L L W L W 4 0 0 4 0 4 W L L W W L 4 0 0 4 4 0 W L L W D D 4 0 0 4 2 2 W L W L L W 4 0 4 0 0 4 W L W L W L 4 0 4 0 4 0 W L W L D D 4 0 4 0 2 2 W L D D L W 4 0 2 2 0 4 W L D D W L 4 0 2 2 4 0 W L D D D D 4 0 2 2 2 2 D D L W L W 2 2 0 4 0 4 D D L W W L 2 2 0 4 4 0 D D L W D D 2 2 0 4 2 2 D D W L L W 2 2 4 0 0 4 D D W L W L 2 2 4 0 4 0 D D W L D D 2 2 4 0 2 2 D D D D L W 2 2 2 2 0 4 D D D D W L 2 2 2 2 4 0 D D D D D D 2 2 2 2 2 2
Six teams are to play against each other once in a tournament. How many matches will be played?
Let me name each team as A, B, C, D, E, F.So, lets start counting number of matches played by each team one after the other.1. Team A will play with B, C, D, E, F. So number of matches played by team A is equal to 5.2. Team B will play with C, D, E & F.( Team B & A have already played match with each other. So we won't count it again.) So, number of matches played by team B is equal to 4.3. Team C will play with D, E, F & as it has already played with B & A, we will not count it again. So, number of matches played by team C is equal to 3.4. Team D is left to play with E & F as it has already played with rest of the team. So, number of matches played by team D is equal to 25. Team E & F will play with each other.Add total number of matches played from above which is equal to 5 +4+3+2+1=15From here, further matches to be played will be based on how many teams will qualify for next round.1st scenario:4 teams reached semis based on Points table. So 2 semis & 1 Final.So total number of matches played in the tournament is 15+3= 18.2nd scenario :Only 2 teams qualifies for Final. So, total number of matches played in the tournament is 15+1=16.Hope it helps!!
Does anyone know to play taboo? I have the game, but lost the directions?
The taboo cards come in several different categories. You have to describe the word WITHOUT actually using the word. Hand gestures, sound effects, and 'sounds like' clues are not allowed. Song lyrics, fill in the blanks, suggestive sentences are. (ie. the word on the dictionary card is TIME - you could say: 1) it is eternal 2) it heals all wounds 3) it is a popular magazine 4) there are many of these zones across the world, 5) math has a table based on this...and so on OBJECT: Score the most points by guessing the most words. DIRECTIONS: Step 1: Divide the players into two teams. Place the buzzer and cards in the center of the table. Step 2: Choose one person from a team to be the first clue giver. She sits opposite her team and draws a card and starts the timer. The card should be hidden from her team but visible to at least one of her opponents. That opponent should hold the buzzer. Step 3: Give clues, as the clue giver, to the players on your team. The clues can be single words or sentences. The clue giver cannot use any word from the Taboo list printed on the card. Any parts of those words or forms of those words are also forbidden. For example, if the forbidden word is "birthday," the clue giver cannot use "birth" or day." If the forbidden word is "read," the clue giver cannot use "reading." Step 4: Score one point for the clue giver's team for each word they guess correctly. There is no penalty for wrong answers. Step 5: Award one point to the clue giver's opponents for each time a Taboo word is used, and for each time the clue giver passes on a word. Step 6: Hit the buzzer if the clue giver uses a Taboo word. Then the clue giver moves onto a new word.
Out of 22 matches, in how many ways can you predict the outcome of 18 matches correctly if the outcomes are win, lose or draw?
22C18 × 3^18