Student examination

How many ways can a teacher select a group of 6 students to sit in the front row if the class has 13 students?

Correct answer:

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Someone

the question doesnt say that the ordering doesnt matter, so wouldnt that mean the answer would be 13P6 or 1235520 ways?

1 year ago 2 Likes Like

Dr. Math

To determine the number of ways a teacher can select a group of 6 students from a class of 13 students, we will use the concept of combinations. Combinations are used when the order of selection does not matter.

Step 1: Understand the Problem
We need to select 6 students out of 13, and the order in which they are selected does not matter. This is a combination problem.

Step 2: Recall the Combination Formula
The number of ways to choose k items from n items is given by the combination formula:

C(n, k) = n!/k!(n - k)!,

where:
- n! (n factorial) is the product of all positive integers up to n ,
- k! is the factorial of k ,
- (n - k)! is the factorial of (n - k) .

Step 3: Substitute the Values
Here, n = 13 (total students) and k = 6 (students to select). Substitute these values into the formula:

C(13, 6) = 13!/6!(13 - 6)! = 13!/6! · 7!.

Step 4: Simplify the Factorials
We can simplify the factorials by canceling out common terms:

C(13, 6) = 13 × 12 × 11 × 10 × 9 × 8 × 7!/6! × 7!.

The 7! terms cancel out:

C(13, 6) = 13 × 12 × 11 × 10 × 9 × 8/6!.

Now, calculate 6! :

6! = 6 × 5 × 4 × 3 × 2 × 1 = 720.

Step 5: Calculate the Numerator
Calculate the numerator:

13 × 12 = 156,

156 × 11 = 1716,

1716 × 10 = 17160,

17160 × 9 = 154440,