A teacher prepares a test. 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 question have 3 chioce and the last 3 have 4 choices.

I think this a permutation question need help

This is a combination question, since the order in which the questions are answered is not important.

All students have to answer 4 questions out of 5, which means that students can skip exactly one question, any single question.

So there are two cases:
Either
1. the student answers 1 question out of the first 2, and 3 questions out the the last 3,
or
2. the student answers 2 questions out of the first 2 and 2 questions out of the last 3.

Case 1:
There are 3 choices in question 1 or 2, 4 choices each in the remaining 3 questions, so the number of answers for the particular choice of questions is 3*4*4*4=192.
The number of choices of questions is
(2,1)=2 for the first group, and (3,3)=1
for a total of 2*1=2 choices of questions for case 1.
The total number of answers for case can be found by multiplying the number of choice of questions with the number of possible answers for each selection of questions = 2*192=384.

Case 2:
Number of possible answers for each selected combination of questions
= 3*3*4*4 = 144
Number of possible choice of questions:
(2,2)*(3,2)=1*3=3
Total number of possible answers for case 2 = 144*3=432

Total possible answers = 384+432 = 816

Yes, you are correct. This is a permutation question because the order of answering the questions matters. We can solve this problem step by step.

First, let's calculate the number of ways to choose which 4 questions out of 5 will be answered. Since there are 5 questions and we need to select 4, we can use the combination formula:

C(5, 4) = 5! / (4!(5-4)!) = 5

Next, let's consider the choices for the first 2 questions. We have 3 choices for each of these questions. Since the order matters, we can calculate the number of ways to choose these 2 questions:

3 choices for the first question * 3 choices for the second question = 3 * 3 = 9

Finally, let's consider the choices for the last 3 questions. We have 4 choices for each of these questions. Since the order matters, we can calculate the number of ways to choose these 3 questions:

4 choices for the third question * 4 choices for the fourth question * 4 choices for the fifth question = 4 * 4 * 4 = 64

Therefore, the total number of ways to answer the questions is:

Total ways = number of ways to choose 4 questions * number of ways to choose the first 2 questions * number of ways to choose the last 3 questions
= 5 * 9 * 64
= 2,880

So, there are 2,880 ways in which the students can answer the questions.

To solve this problem, we can use the concept of permutations. The total number of ways to answer the questions can be found by multiplying the number of choices for each question together.

First, let's consider the two questions with 3 choices. Since each question has 3 choices, there are 3*3 = 9 ways to answer these two questions.

Now, let's consider the last three questions with 4 choices each. Since each question has 4 choices, there are 4*4*4 = 64 ways to answer these three questions.

To find the total number of ways to answer the 4 questions, we multiply the number of ways to answer the first two questions by the number of ways to answer the last three questions: 9 * 64 = 576.

Therefore, there are 576 total ways in which the 4 questions can be answered.