Question

5 questions are asked in a question paper out of which two questions can be solved with two-two methods, two questions can be solved with three-three methods and one question can be solved by only one method then the number of possible attempts to solve the question paper are?
A. $2^2$
B. $2^2\cdot 3^2\cdot 1^2$
C. 144
D. 288

Answer 1

Hint: The number of possible attempts here means the number of ways in which the paper can be solved. As such, find the number of possible methods in which each question can be solved and then multiply the same to get every permutation and combination possible.

Complete step by step solution:
In this question, first let us take 5 alphabets which will represent our five questions asked in the question paper. So, we name them A, B, C, D and E.
Say A and B are the questions which can be solved by two methods each.
C and D are the ones which have solutions laid to 3 methods each.
Finally, there is E which has only one method to solve the question.
Thus, we can write the same as this.

Now multiplying the numbers written below, we get the result which is $2^2\cdot 3^2\cdot 1$ which when observing the options relates to option ‘b’ as $1^2=1$.

As such from the options, the number of attempts that can be done is $2^2\cdot 3^2\cdot 1^2$.

Note:
Whenever solving such questions, adding the number of ways will give the wrong answer because the questions are not being attempted in any set pattern and as such the randomness of selection of question as well as the method to solve it can be dealt with by multiplication only.