Seven people chosen for Kho -Kho team from a group of 8 boys and 6 girls .In how many ways 3 boys and 4 girls can be chosen for Kho -Kho team ?
खो-खो टीम के लिए 8 लड़कों और 6 लड़कियों के समूह में से सात लोगों को चुना गया। खो-खो टीम के लिए 3 लड़कों और 4 लड़कियों को कितने तरीकों से चुना जा सकता है?

Options

A. 92
B. 696
C. 768
D. 840

Answer

To solve the problem of choosing 3 boys and 4 girls for a Kho-Kho team from a group of 8 boys and 6 girls, we can use the concept of combinations.

### Step-by-Step Solution:

1. **Identify the total number of boys and girls:**
- Total boys = 8
- Total girls = 6

2. **Determine how many boys and girls we need to choose:**
- Boys to choose = 3
- Girls to choose = 4

3. **Calculate the number of ways to choose 3 boys from 8 boys:**
- The number of ways to choose 3 boys from 8 is given by the combination formula:
\[ \text{C}(n, r) = \frac{n!}{r!(n-r)!} \]
- Here, \( n = 8 \) and \( r = 3 \):
\[ \text{C}(8, 3) = \frac{8!}{3!(8-3)!} = \frac{8!}{3! \cdot 5!} \]
- Expanding this gives:
\[ \text{C}(8, 3) = \frac{8 \times 7 \times 6}{3 \times 2 \times 1} = \frac{336}{6} = 56 \]

4. **Calculate the number of ways to choose 4 girls from 6 girls:**
- The number of ways to choose 4 girls from 6 is:
\[ \text{C}(6, 4) = \frac{6!}{4!(6-4)!} = \frac{6!}{4! \cdot 2!} \]
- Expanding this gives:
\[ \text{C}(6, 4) = \frac{6 \times 5}{2 \times 1} = \frac{30}{2} = 15 \]

5. **Calculate the total number of ways to form the team:**
- Since the choices of boys and girls are independent, we multiply the number of ways to choose boys by the number of ways to choose girls:
\[ \text{Total ways} = \text{C}(8, 3) \times \text{C}(6, 4) = 56 \times 15 \]
- Performing the multiplication:
\[ 56 \times 15 = 840 \]

### Final Answer:
The total number of ways to choose 3 boys and 4 girls for the Kho-Kho team is **840**.

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