A question paper has two parts P and Q, each containing 10 questions. If a student needs to choose 8 from part P and 4 from part Q, in how many ways can he do that?Choices:- 1200 9450 6020 None of these
Question
A question paper has two parts P and Q, each containing 10 questions. If a student needs to choose 8 from part P and 4 from part Q, in how many ways can he do that?Choices:- 1200 9450 6020 None of these
Solution
The problem can be solved using the concept of combinations in probability.
In part P, the student has to choose 8 questions out of 10. This can be done in 10C8 ways.
In part Q, the student has to choose 4 questions out of 10. This can be done in 10C4 ways.
The total number of ways to choose the questions is the product of the number of ways to choose from each part, because the choices in part P and part Q are independent.
So, the total number of ways = 10C8 * 10C4
Using the formula for combinations nCr = n! / [(n-r)! * r!], where n is the total number of items, r is the number of items to choose, and "!" denotes factorial,
10C8 = 10! / [(10-8)! * 8!] = 45 10C4 = 10! / [(10-4)! * 4!] = 210
So, the total number of ways = 45 * 210 = 9450
So, the student can choose the questions in 9450 ways. The correct answer is 9450.
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