A school debate team has 4 girls and 6 boys. A total of 4 of the team members will be chosen to participate in the district debate. What is the probability that 2 girls and 2 boys will be selected?
A.3/7
B.4/10
C.1/14
D.1/210
3/7
To find the probability of selecting 2 girls and 2 boys from the debate team, we need to determine the total number of possible outcomes and the number of favorable outcomes.
To begin, we'll calculate the total number of possible outcomes. Since there are a total of 10 team members, the total number of possible outcomes is given by the combination formula:
nCr = n! / (r!(n - r)!)
where n is the total number of items to choose from (10 team members) and r is the number of items we need to choose (4 members for the debate).
Using this formula, we can calculate the total number of possible outcomes:
10C4 = 10! / (4!(10 - 4)!)
= 10! / (4! * 6!)
= (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)
= 210
Next, we'll determine the number of favorable outcomes, which is the number of ways to select 2 girls and 2 boys.
We'll calculate the number of ways to select 2 girls from the 4 available, which is given by the combination formula:
4C2 = 4! / (2!(4 - 2)!)
= 4! / (2! * 2!)
= (4 * 3) / (2 * 1)
= 6
Similarly, we'll calculate the number of ways to select 2 boys from the 6 available:
6C2 = 6! / (2!(6 - 2)!)
= 6! / (2! * 4!)
= (6 * 5) / (2 * 1)
= 15
Now, to calculate the total number of favorable outcomes, we multiply the number of ways to select 2 girls and 2 boys:
Total number of favorable outcomes = (Number of ways to select 2 girls) * (Number of ways to select 2 boys)
= 6 * 15
= 90
Finally, we can obtain the probability by dividing the total number of favorable outcomes by the total number of possible outcomes:
Probability = (Total number of favorable outcomes) / (Total number of possible outcomes)
= 90 / 210
= 3 / 7
Therefore, the probability that 2 girls and 2 boys will be selected is 3/7.
Hence, the correct answer is A. 3/7.
Cheater
Choosing 2 girls from the 4 --- C(4,2)
Choosing 2 boys from the 6 --- C(6,2)
choosing any 4 of the 10 --- C(10,4)
make use of that