Probability

-if desks are grouped by 4 and if there are 11 boys and 13 girls in a class what is the probability that I will get placed in a group of all girls?

i mean, I know how to do 1 like the probability of getting paired with someone but how does the 4 come in?

because the amount of desks are 4

no, but i mean how do you factor the probability of 4 instead of just 1?

To calculate the probability of being placed in a group of all girls, you need to determine the total number of possible groups and the number of groups that consist entirely of girls.

Let's start by calculating the total number of possible groups. Since desks are grouped by 4, the total number of groups will be the total number of students divided by 4.

Total number of students = 11 boys + 13 girls = 24 students
Total number of possible groups = 24 students / 4 students per group = 6 groups

Now, let's determine the number of groups that consist entirely of girls. Since there are 13 girls in the class, we need to calculate the number of groups that can be formed with 4 girls.

Number of groups with all girls = (Number of girls choose 4)

To calculate the number of groups that can be formed, we can use the combination formula:

C(n, r) = n! / (r! * (n - r)!)

Where n is the total number of girls and r is the number of girls needed to form a group (in this case, 4).

Number of groups with all girls = C(13, 4) = 13! / (4! * (13 - 4)!)

Using the factorial notation, we can simplify the equation:

Number of groups with all girls = 13! / (4! * 9!)
= (13 * 12 * 11 * 10) / (4 * 3 * 2 * 1)
= 13 * 11 * 10 / (3 * 2 * 1)
= 1,430

Now, we can calculate the probability of being placed in a group of all girls:

Probability = (Number of groups with all girls) / (Total number of possible groups)
= 1,430 / 6
= 238.3 (rounded to the nearest whole number)

Therefore, the probability of being placed in a group of all girls is approximately 238 out of 1000, or approximately 23.8%.