Heres a challenge:
six students(4 boys and girls) were divided into three pairs. given this information. What is the probability of 2 girls making 1 pair? Express as a common fraction.
Oh and please explain!!
can someone please help me...
x equals the opposite of b plus or minus the square root of b squared minus four a c all over 2 a
To find the probability of 2 girls making 1 pair out of the six students, we need to first determine the total number of possible pairings.
Considering that there are 4 girls and 2 boys, we can think of the problem from a combination perspective. We have 6 students and need to select 2 for the first pair, which can be done in C(6, 2) ways (read as "6 choose 2"). The number of ways to choose 2 from 6 can be calculated using the combination formula:
C(n, r) = n! / (r! * (n - r)!)
In this case, C(6, 2) = 6! / (2! * (6 - 2)!) = 6! / (2! * 4!) = (6 * 5) / (2 * 1) = 15.
After forming the first pair, we are left with 4 students. For the second pair, we need to select 2 students from the remaining 4, which can be calculated as C(4, 2) = 4! / (2! * (4 - 2)!) = 4! / (2! * 2!) = 6.
Finally, for the third pair, we only have 2 students left, so we only have one option for the pair.
To find the total number of possible pairings, we multiply the number of ways to select students for each pair:
Total number of pairings = C(6, 2) * C(4, 2) * 1 = 15 * 6 * 1 = 90.
Now that we know the total number of pairings, we can find the number of pairings where 2 girls make 1 pair.
To form a pair with 2 girls, we first need to choose 2 girls from the 4 available. This can be done in C(4, 2) ways = 4! / (2! * (4 - 2)!) = 4! / (2! * 2!) = 6.
After selecting 2 girls for the pair, we have 4 students remaining. The remaining 2 boys and 2 girls can be paired in 1 way.
The number of pairings with 2 girls making 1 pair is: C(4, 2) * 1 = 6 * 1 = 6.
Therefore, the probability of 2 girls making 1 pair is:
Probability = (Number of pairings with 2 girls making 1 pair) / (Total number of pairings) = 6 / 90 = 1 / 15.
So, the probability of 2 girls making 1 pair is expressed as the common fraction 1/15.