Out of 8 outstanding students of school, in which there are 3 boys and 5 girls, a team of 4 students is to be selected for a quiz competition. Find the probability that 2 boys and 2 girls are selected.

Answer

To solve the problem of finding the probability that a team of 4 students selected from 3 boys and 5 girls consists of 2 boys and 2 girls, we can follow these steps:

### Step 1: Calculate the Total Number of Ways to Select 4 Students
We need to find the total number of ways to select 4 students from the 8 outstanding students (3 boys and 5 girls). This can be calculated using the combination formula:

\[ \text{Total ways} = \binom{8}{4} \]

Calculating this:

\[ \binom{8}{4} = \frac{8!}{4!(8-4)!} = \frac{8 \times 7 \times 6 \times 5}{4 \times 3 \times 2 \times 1} = 70 \]

### Step 2: Calculate the Number of Favorable Outcomes for 2 Boys and 2 Girls
Next, we need to find the number of ways to select 2 boys from the 3 available boys and 2 girls from the 5 available girls. This can be calculated as follows:

\[ \text{Ways to select 2 boys} = \binom{3}{2} \]
\[ \text{Ways to select 2 girls} = \binom{5}{2} \]

Calculating these:

\[ \binom{3}{2} = \frac{3!}{2!(3-2)!} = \frac{3}{1} = 3 \]
\[ \binom{5}{2} = \frac{5!}{2!(5-2)!} = \frac{5 \times 4}{2 \times 1} = 10 \]

### Step 3: Calculate the Total Number of Favorable Outcomes
Now, we multiply the number of ways to select the boys and girls:

\[ \text{Favorable outcomes} = \binom{3}{2} \times \binom{5}{2} = 3 \times 10 = 30 \]

### Step 4: Calculate the Probability
Finally, we can find the probability of selecting 2 boys and 2 girls by dividing the number of favorable outcomes by the total number of outcomes:

\[ \text{Probability} = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{30}{70} = \frac{3}{7} \]

### Final Answer
The probability that 2 boys and 2 girls are selected is:

\[ \frac{3}{7} \]