A women student is to answer 10 out of 13 questions.Find the number of her choices where she must answer exactly 3 out of 5 questions?
To find the number of choices where the women student must answer exactly 3 out of 5 questions, we can use combinations.
In this case, we have 5 questions and the student must answer exactly 3 of them. The remaining 2 questions can be left unanswered.
The formula to calculate combinations is:
C(n, r) = n! / (r! * (n - r)!)
Where:
- n is the total number of items (in this case, 5 questions)
- r is the number of items chosen (in this case, 3 questions)
Plugging the values into the formula, we have:
C(5, 3) = 5! / (3! * (5 - 3)!)
= 5! / (3! * 2!)
= (5 * 4 * 3!) / (3! * 2 * 1)
= (5 * 4) / 2
= 10
Therefore, there are 10 different choices where the women student can answer exactly 3 out of the 5 questions.