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An examination consists of 10 multiple choice questions, where each question has 4 options, only one of which is correct. In every question, a candidate earns 3 marks for choosing the correct opion, and -1 for choosing a wrong option. Assume that a candidate answers all questions by choosing exactly one option for each. Then find the number of distinct combinations of anwers which can earn the candidate a score from the set {15, 16,17,18, 19, 20}. |
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Answer» `therefore` His score is `3x+(10-x)(-1)=4x-10` Now score of the candidate is from the set {15,16,17,18,19,20}. Only 4x-10=18 is possible . `therefore x=7` So, his 7 answer are CORRECT and 3 answers are wrong. Number of ways of selection of 7 questions from `10= .^(10)C_(7)= .^(10)C_(3)` `=(10xx9xx8)/(6)=120` |
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