A teacher prepares a lest. She gives 5 objective type questions out of which 4 have to be answered. Find the total ways in which they can be answered if the first 2 questions have 3 choices and the last 3 have 4 choices.
First 2 questions: Each of the first 2 questions has 3 choices.
Number of ways to choose and answer 2 out of these 2 questions =
3 ×3=9
3×3=9 ways.
Last 3 questions: Each of the last 3 questions has 4 choices.
Number of ways to choose and answer 2 out of these 3 questions =
4×4×4=64
4×4×4=64 ways.
Total number of ways: We need to multiply the number of ways to choose and answer the questions from each group.
Total ways =9×64=576
9×64=576.
Therefore, the total number of ways in which the teacher's test can be answered, given the choices for each question, is 576
ChatGPT
To find the total number of ways the 4 out of 5 objective questions can be answered, considering the choices provided:
First 2 questions: Each of the first 2 questions has 3 choices.
Number of ways to choose and answer 2 out of these 2 questions =
3
×
3
=
9
3×3=9 ways.
Last 3 questions: Each of the last 3 questions has 4 choices.
Number of ways to choose and answer 2 out of these 3 questions =
4
×
4
×
4
=
64
4×4×4=64 ways.
Total number of ways: We need to multiply the number of ways to choose and answer the questions from each group.
Total ways =
9
×
64
=
576
9×64=576.
Therefore, the total number of ways in which the teacher's test can be answered, given the choices for each question, is
576
576
.
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