Question 92750: Please help me explain thoroughly the answer to the following questions? thank you so much
Consider a multiple-choice exam with 15 items and each item has 3 choices. and a student must answer all the items:
a) in how many ways can the student answer it and all his/her answers are correct?
b.) In how many ways can a student answer the exam and answer exactly four items correctly?
c) In how many ways can a student answer the exam and answer at least one(1) item correctly?
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! there are 15 questions with 3 possible choices for each, this means that there are 3^15 different combinations of answers
a.) assuming only one correct choice for each question, there is only ONE combination of all correct answers (1^15)
b.) the number of different groups of 4 items contained in a group of 15 is (15*14*13*12)/(4*3*2*1) ... there are 15 ways to select the first item, 14 ways to select the second, etc. ... the numerator of the expression results from the fact that order is NOT important ... a,b,c,d is the same group as b,a,d,c
c.) there are 15 questions with 2 possible wrong choices for each, this means that there are 2^15 ways to get EVERY question wrong ... since there are 3^15 combinations of answers, there are ((3^15)-(2^15)) ways to get at least one item correct
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