There are two rows of seats in the classroom and each row has six seats. If a class has nine students, and among them three female students G1, G2 and G3 always sit in the first row, two male students B1, B2 always sit in the second row. In how many different ways can all the nine students sit in the classroom?

Question

There are two rows of seats in the classroom and each row has six seats. If a class has nine students, and among them three female students G1, G2 and G3 always sit in the first row, two male students B1, B2 always sit in the second row. In how many different ways can all the nine students sit in the classroom?

Answer 1

6x 35= 210

Answer 2

Wrong answer.

Answer 3

1 of 51 of 5 Items

Question
In an art classroom, 8 students can sit around 1 table, and 48 students can sit around 6 tables. What is the relationship between the number of students to tables in fraction form? Write the proportion in fraction form without reducing it to the lowest terms.
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Answer 4

To find the number of different ways the nine students can sit in the classroom, we need to consider the seating arrangements for each group of students. Let's break it down step by step:

1. The three female students, G1, G2, and G3, always sit in the first row. There are three seats in the first row, and since the order doesn't matter among these three students, we can calculate the arrangement using combinations. So, the number of ways these three students can sit is represented by the combination formula: C(n, k) = n! / (k!(n-k)!), where n is the number of seats (3) and k is the number of students (3). In this case, C(3, 3) = 3! / (3!(3-3)!) = 1 way.

2. The two male students, B1 and B2, always sit in the second row. There are also three seats in the second row, but since the order doesn't matter among these two students, we again use the combination formula. So, the number of ways these two students can sit is represented by C(n, k) = n! / (k!(n-k)!), where n is the number of seats (3) and k is the number of students (2). In this case, C(3, 2) = 3! / (2!(3-2)!) = 3 ways.

3. After accommodating the first group of students, we are left with four students and four empty seats. We can arrange them in the remaining seats in a total of 4! = 4 x 3 x 2 x 1 = 24 ways.

Now, to find the total number of ways the nine students can sit in the classroom, we multiply the number of ways in each step together:

Total ways = 1 way (for the first row) × 3 ways (for the second row) × 24 ways (for the remaining seats) = 72 ways.

Therefore, there are 72 different ways in which all the nine students can sit in the classroom.