Appearance
question:How many different ways can you select a team of 4 from 11 possible players so that 2 of the selected players are from 3 defenders and the other 2 selected are from 8 non-defenders on the team and one of those selected non-defenders must be the captain.
answer:To form a team with the given conditions, we need to select 2 players from the 3 defenders and 2 players from the 8 non-defenders, with one of the non-defenders being the captain. We can start by selecting 2 players from the 3 defenders. This is a combination problem, and we can calculate the number of ways to do this using the combination formula: (n choose k) = n! / (k!(n-k)!), where n is the total number of items, k is the number of items to choose, and ! denotes factorial. For the defenders, we have (3 choose 2) = 3! / (2!(3-2)!) = 3. Next, we need to select 2 non-defenders, including the captain. We can first select the captain, which can be done in 1 way (since there is only 1 captain), and then we need to choose 1 more non-defender from the remaining 7 non-defenders. This can be done in (7 choose 1) = 7 ways. However, to correctly obtain the number of combinations for the non-defenders, we need to multiply the initial (7 choose 1) by 1, which is the same as selecting the captain, but consider (8 choose 1) for selecting the captain first, followed by (7 choose 1) for the second selection. This way, we form the total possible non-defender groups with a chosen captain: (1 choose 1)*(7 choose 1) can be equivalently and correctly put as (8 choose 1)*(7 choose 1)/(2 choose 1) for choosing a total of 2 players in a group = (8 choose 2) is not correct here because there isn't any equivalent arrangement between 2 chosen players when one is specifically a captain (thus leading to overcount error and correct expression should multiply with different noncaptain non-defender combinations). Since there are (8 choose 1) = 8 ways to select the captain, the total ways we can choose the non-defenders is (8 choose 1)*(7 choose 1)/(2 choose 1) ((8 choose 1)times (7 choose 1)) (=8times7=56). Now multiply the total number of ways to select defenders with the total number of ways to select non-defenders: 3 * 56/2 = (3 times 28 = 84).
question:Why is the number 28? , why divide by 2
answer:The reason for dividing by 2 in the previous response was incorrect. When we choose the captain (8 choose 1) and then another non-defender (7 choose 1), we get a total of 8 * 7 = 56 combinations. However, this calculation is correct. The number 28 was introduced due to an incorrect division by 2. The correct calculation should simply multiply the number of ways to choose defenders by the number of ways to choose non-defenders, which is 3 * 56. So, the correct total number of ways to select a team of 4 from 11 possible players, with 2 defenders and 2 non-defenders, including the captain, is indeed 3 * 56 = 168.
question:New York (CNN)New York City's longest recorded homicide-free streak ended late Friday night, when a 28-year-old man was shot multiple times just before midnight. Eric Roman was transported to a nearby hospital in critical condition with gunshot wounds to his head, hand and leg and died Saturday, according to the New York Police Department. New York City had gone 12 days without a homicide, its longest stretch on modern record, police said Monday. The last reported homicide was February 1, Super Bowl Sunday, in Upper Manhattan, police said. That day, police responded to a 911 call about multiple shots being fired and found five individuals with gunshot wounds, the NYPD said. One of those five, Graham Shadale, 28, was pronounced dead at the scene. Police have not yet made arrests in either case and both investigations are ongoing, officials said. The streak has been the longest since the New York Police Department began recording statistics with a computerized program called Compstat in 1994, a police representative said. Police Commissioner Bill Bratton hushed talk of the streak Friday on CBS This Morning. Shh ... we don't want to jinx it, Bratton told host Charlie Rose. We're into our 12th day now, Charlie. Eleven is a record and let's keep it going. Despite the record-breaking streak, there has been an uptick in shooting incidents compared with the same time period last year. The week between February 1 and February 8 experienced 110 shooting incidents in 2015 versus 91 in 2014, according to Detective Cheryl Crispin of the NYPD public information office. New York City's last record for a streak of days without a homicide was 10 days. In 2014, there were no recorded homicides between February 13 and February 22. CNN's Lorenzo Ferrigno contributed to this report.
answer:New York City's longest recorded homicide-free streak, which lasted 12 days, ended late Friday night when 28-year-old Eric Roman was shot multiple times and died the following day. The previous homicide, on February 1, involved five individuals with gunshot wounds, one of whom, Graham Shadale, 28, died at the scene. Both cases remain under investigation, and no arrests have been made. Police Commissioner Bill Bratton had cautiously acknowledged the streak on CBS This Morning, hoping to maintain it. Despite the record-breaking period, there has been an increase in shooting incidents compared to the same time last year, with 110 shootings between February 1 and February 8, 2015, up from 91 in 2014. The previous longest homicide-free period was 10 days, recorded in 2014.
question:Hi Alex, I hope this email finds you well! It's been a while since we connected at the ELL conference last year. I recently accepted a new position at a bilingual language clinic in San Francisco and will be moving there with my family next month. My husband and I are currently researching schools for our daughter, Emma, who will be starting kindergarten in the fall. Given your expertise in working with bilingual students, I was wondering if you had any recommendations for schools in the area that have strong language support and a diverse student population. I'd also love to catch up on your latest projects and hear more about the art unit you mentioned during our last conversation. If you have time, perhaps we could schedule a virtual coffee chat sometime next week? Looking forward to hearing back from you! Best regards, Lily Chen, MS, CCC-SLP
answer:Lily, who recently accepted a position at a bilingual language clinic in San Francisco, is looking for recommendations on schools with strong language support and a diverse student population for her daughter, Emma, who will start kindergarten in the fall. She also hopes to catch up on the latest projects and discuss the art unit mentioned in a previous conversation, suggesting a virtual coffee chat next week.