9) A 16-sided die shows a different number of dots, from 1 to 16, on each face. Suppose we roll this die 10 times and we record the number of dots that come up on each roll. a) How many possible outcomes are there if an outcome is represented by an ordered l-tuple, where the ith coordinate states the number ofdots on the ith toss, i=1,2....,10? b) How many among the outcomes in (a) satisfy the condition that the number of dots are distinct in all 10 tosses? c) How many among the outcomes in (b) satisfy the condition that the number of dots decreases after each roll. d) How many among the outcomes in (c) satisfy the condition that that the number of dots on the first roll is a 14, on the second roll is a 13, and on the third roll is a 10? e) How many among the outcomes in (a) satisfy the condition that the number of dots is less than Bin at least 4 of the 10 rolls? D How many among the outcomes in (a) satisfy the condition that the number ofdots is from 1 to 5 in exactly 3 tosses, the number of dots is from 6 to 12 in exactly 5 tosses, and the number of dots is from 13 to 16 in exactly 2 tosses? 10) In the School of Statistics where only 450 students are enrolled. there are 120 who are taking Bio 1. 200 who are taking Chem Land there are 5'5 who are taking Arts 1. A total of 50 are taking all these subjects while 200 are not enrolled in any one of these subjects. There are 60 who are enrolled in Arts 1 and Bin 1 and there are also 65 who are enrolled in Arts 1 and Chem 1. Let =set of School of Statistics enrolled students A=set of students taking Arts 1 B=set ofstudents taking Bin 1 C=set of students taking Chem 1 in each item, express the set whose nite cardinal we are looking for in terms of the dened sets. A. B, and C. Use the given information and the theorems on the cardinals of new sets formed through set operations in our course notes to solve the problems. Show all steps in solving the problems. It must be clear in the solution which theorem/s presented in our lecture was used to answer the question. a) How many are taking at least one of the three subjects? b) How many are taking at least one of Arts 1 and Bin 1? c) How many are taking in Bio 1 and Chem 1? d) How many are taking Arts 1 and Chem 1. but not Bio 1? e) How many are taking Arts 1 and at least one of Chem 1 and Bin 1