Question

One student moved to another town before Ms. Brunswick took the pictures. since there are now 20 students, she has decided to have 2 students in each picture. how many ways could the students group themselves into twos if the order in which they are standing does not matter?

Answer 1

The number of ways 20 students can group themselves into pairs without considering the order is 190, calculated using the combination formula C(20, 2).

Step-by-step explanation:

The student is asking about the number of ways 20 students can group themselves into pairs for pictures, where the order in which they stand does not matter. This type of problem is known as a combination problem in mathematics, specifically combinatorial mathematics. To solve this, we can use the combination formula which is defined as C(n, k) = n! / (k!(n - k)!), where n is the total number of items, k is the number of items to choose, '!' denotes factorial, and 'C' is the combination.

To find the number of ways to pair 20 students, we are looking for combinations of 20 taken 2 at a time (since each picture has 2 students). Applying the combination formula, we get:

C(20, 2) = 20! / (2!(20 - 2)!)
= 20! / (2!18!)
= (20 × 19) / (2 × 1)
= 190

There are 190 different ways the students can pair up for pictures.