If a test contains 150 questions and each question contains 5 options find the total number of ways in which a student can answer at least 2 out of 150
Answers
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Given: Total number of questions = 150
Number of options in each question = 5
To find: The total number of ways in which a student can answer at least 2 out of 150
Solution: The number of ways in which a student can answer a question = 6 (since there are 5 options to answer from and there is a chance of not answering at all.)
Therefore, the total number of ways to answer the questions = 6¹⁵⁰.
Now, we need to deduct some of ways from this which are as follows.
The number of ways to answer no question at all = 1.
The number of ways to answer only one question = 150 × 5 = 750.
Hence, the total number of ways in which a student can answer at least 2 out of 150 = 6¹⁵⁰ - (1 + 750)
= 6¹⁵⁰ - 751.
Answer: 6¹⁵⁰ - 751