The question asks for the number of ways in which four boys and four girls can sit alternately in a row. Let's solve this step by step:

Step 1: Understanding the arrangement

• Alternate seating means the arrangement must follow one of these patterns:
  • Boy, Girl, Boy, Girl, Boy, Girl, Boy, Girl
  • Girl, Boy, Girl, Boy, Girl, Boy, Girl, Boy

Step 2: Arranging the boys and girls

• Arrangements of boys: The four boys can be arranged among themselves in $4! = 24$ ways.
• Arrangements of girls: The four girls can be arranged among themselves in $4! = 24$ ways.

Step 3: Arrangements of the overall pattern

• There are 2 alternate patterns (Boy-Girl or Girl-Boy). Hence, the total number of ways to alternate the arrangement is:

$2 \times (4! \times 4!) = 2 \times 24 \times 24 = 1152$

Final Answer:

The total number of ways in which four boys and four girls can sit alternately in a row is 1152.

Let me know if you'd like a more detailed explanation or have any questions! Here are some related problems for practice:

1. How many ways can 3 boys and 3 girls sit alternately in a circle?
2. What happens if the boys and girls cannot sit alternately but must stay together as groups?
3. If one boy and one girl must always sit next to each other, how does that change the arrangement count?
4. What if one specific boy and girl refuse to sit next to each other? How does that affect the solution?
5. How many ways can 5 boys and 5 girls sit alternately?

Tip: When dealing with seating arrangements, always consider symmetry or repetition to simplify calculations!