In a question paper there are two parts A and B . Part A contains 6 questions and part B contains 7 questions . in how many ways a student can select 4 questions in part A of which 2 questions are compulsory and 5 questions in part B of which 3 questions are compulsory ?????PLZZZ SOLVE THIS
I tried but it is fruitless
4C2 x 4 C2 = 36
How please explain
10 question out of 13 question to answer
To solve this problem, we can use a combination formula to calculate the number of ways a student can select the questions.
In Part A, there are 6 questions. 2 of them are compulsory, so we need to select 2 questions out of the remaining 6 - 2 = 4 questions.
The number of ways to select 2 questions out of 4 can be calculated using the combination formula:
C(n, r) = n! / (r!(n-r)!)
Where n represents the total number of items, and r represents the number of items to be selected.
Using the combination formula, we can calculate the number of ways to select 2 questions out of 4 in Part A:
C(4, 2) = 4! / (2!(4-2)!)
= 4! / (2!2!)
= (4 * 3 * 2!) / (2! * 2!)
= (4 * 3) / 2
= 6
So, there are 6 ways to select 2 questions out of 4 in Part A.
Similarly, in Part B, there are 7 questions and 3 of them are compulsory. We need to select 3 questions out of the remaining 7 - 3 = 4 questions.
Using the same combination formula, we can calculate the number of ways to select 3 questions out of 4 in Part B:
C(4, 3) = 4! / (3!(4-3)!)
= 4! / (3!1!)
= 4
So, there are 4 ways to select 3 questions out of 4 in Part B.
Now, to find the total number of ways a student can select the questions, we multiply the number of ways in each part:
Total ways = Number of ways in Part A * Number of ways in Part B
= 6 * 4
= 24
Therefore, there are 24 ways a student can select the questions as per the given conditions.