Let S and T be subsets ofthe universal set U. Draw an appropriate Venn diagram and use the given data to determine the number of elements in each basic region. n(U)=16, ma): 7, n(T) = r: msnr) = 2 Region loontains 4 elements. (Simplify your answer.) Region II contains 5 elements. (Simplify your answer.) Region III contains 2 elements. (Simplify your answer.) Region IV contains 5' elements. (Simplify your answer.) Let 5 and T be subsets ofthe universal set U. Use the Venn diagram on the right and the given data below to determine the number of elements in each basic region. n(U)=18_. n(S)= 1o. n(T}=12, n(SUT)= 15 Region | contains 3 elements. Region II contains 3 elements. Region III contains 7" elements. Region IV contains 5 elements. Draw a three-Circle Venn diagram and shade the portion corresponding to the set (5hr) UR Use the graphing tool to shade the Venn diagram. Click to enlarge graph Click the graph' Choose a tool in the palette and follow the instructio... V \" Selected: none Cancel Save A merchant surveyed 290 people to determine the way they learned about an upcoming sale. The survey showed that 120 learned about the sale from the radio, 150 from television, 100 from the newspaper, 80 from radio and television, 40 from radio and newspapers, 50 from television and newspapers, and 30 from all three sources. How many people learned of the sale from radio or television but not the newspaper? people learned of the sale from radio or television but not the newspaper.\fHow many different possibilities are there for 20 athletes to win first, second, and third places? There are different possibilities.A license plate consists of six symbols on each plate, where the first two symbols are letters of the alphabet and the following four symbols are the digits selected from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}? How many license plates can be produced if any digit or letter can be repeated on any given license plate? waysHow many 5letter code symbols can be formed from the letters from the word RINSE without repetition? How many 5letter code symbols can be formed from the letters from the word RINSE without repetition? D Agroup of 4 boys and 6 girls is to be photographed. (at) How many ways can they be arranged in one row? (b) How many ways can theyr be arranged with the girls in the front row and the boys in the back row\"? (a) What expression should be evaluated to nd the number of ways the boys and girls can be arranged in one row? a! 4! V 10! 4! +6! The boys and girls can be arranged 3.628300' ways in one row. (b) What expression should be evaluated to find the number of ways the boys and girls can be arranged when the girls are in the front row and the boys in the back row\"? 3: 4!+6! 10! * 4!-6! (4-6)! The boys and girls can be arranged in 1?,280' ways when the girls are in the front row and the boys in the back row. 40w many ways can a group of three boys and three girls be seated in a row of six seats if boys and girls must alternate in the row\"? ways How many ways can 5 different contracts be distributed amongst 8 different firms, if any one firm can be awarded multiple contracts? waysAn exam contains 12 "true or false" questions. In how many different ways can the exam be completed? There are different ways the exam can be completed. In a certain country, area codes have four digits and are subject to the following restrictions. The first digit cannot be 0 or 1; the second digit can only be 0, 1, 2, 3, 4, or 5; and there are no restrictions on the remaining digits. How many different area codes are possible? Express the number of area codes as a product. Total number of area codes = (Do not multiply.)Pizza House offers four different salads: seven different kinds of pizza, and four different desserts. How many different three-course meals can be ordered? There are possible combinations. A baseball team has 9 players. How many batting orders are possible under each of the following conditions? Answer parts [a] through {c} below. [a] There are no restrictions. There are D possible batting orders. 40w many threedigit numbers may be formed usrng elements from the set {1, 2, 3, 4' 5; 6} If no element may be used more than once in a number and the number must be even? ways \f\f\fIn how many ways can seven people line up at a single counter to order food at McDonald's? Seven people can line up in D ways. A club with 171 members is to choose three officers - president, vice-president, and secretary-treasurer. If each office is to be held by one person and no person can hold more than one office, in how many ways can those offices be filled? Write the number of ways as a product of factors or as a quotient of products of factors. (Do not multiply.)A signal consists of six flags arranged vertically on a flagpole. If Sally has fourteen flags, each of a different color, how many different signals are possible? Write the number of ways as a product of factors or as a quotient of products of factors. (Do not multiply.)Kristen's nancial adviser has given her a list of 10 potential investments and has asked her to select and rank her favorite four. In how many different ways can she do this? There are different ways Kristen can rank the four investments. (Type a whole number.) A class consists of 12 students (six boys and six girls) and one teacher. In how many ways can the students sit in a circle? waysIf the n objects in a permutations problem are not all distinguishable-that is, if there are n, of type 1, n, of type 2, and The number of possible permutations is n! so on, for r different types-then the number of distinguishable permutations is given by n, In,! . . . n,! How many permutations are possible using the 6 letters in the word LONDON?Find the number of distinguishable permutations of the letters in each word below. (a) palace (b) Alaska (c) referred (a) The number of distinguishable permutations is 360. (Simplify your answer.) (b) The number of distinguishable permutations is 120 (Simplify your answer.) (c) The number of distinguishable permutations is 1120. (Simplify your answer.)