Math

(a)The probability that the student will answer the first six questions correctly and the rest incorrectly is 1/2^10, as there's a one in three chance of picking the correct answer and the student has to get all ten questions wrong to have this outcome. (b)The probability that the student will answer the 1st,2nd,4th,6th,7th, and 10th questions correctly and the rest incorrectly is 1/3^6, as there's a one in three chance of picking the correct answer for each question and the student has to get the other four questions wrong to have this outcome. (c)There are 210 ways for a student to get exactly 6 correct answers out of 10 multiple choice questions. This is calculated by the number of ways to arrange 10 items where 6 of them (the correct answers) are picked out and the other 4 (the incorrect answers) are not picked, which is equal to 10C6 (10 choose 6) = 10!/6!*4! = 10x9x8x7x6x5x4x3x2x1/6x5x4x3x2x1x4x3x2x1 = 210. (d)The probability that the student answers exactly 6 questions correctly is 1/210, as this is the total number of ways the