Step 1: Total number of students is 7 boys + 2 girls = 9 students.

Step 2: The total number of ways to arrange these 9 students is 9 factorial (9!).

Step 3: For the condition where there are exactly 4 boys between the 2 girls, we can consider the 2 girls and the 4 boys between them as a single entity. So, we have 5 entities (this group of 6 and the remaining 3 boys) to arrange, which can be done in 5 factorial (5!) ways.

Step 4: Within this group of 6 (2 girls and 4 boys), they can be arranged in 6 factorial (6!) ways.

Step 5: Therefore, the total number of favorable outcomes is 5! * 6!.

Step 6: The probability is the ratio of the number of favorable outcomes to the total number of outcomes. So, the probability is (5! * 6!) / 9!.

Step 7: Simplify the expression to get the final probability.

Question

Step 1: Total number of students is 7 boys + 2 girls = 9 students.

Step 2: The total number of ways to arrange these 9 students is 9 factorial (9!).

Step 3: For the condition where there are exactly 4 boys between the 2 girls, we can consider the 2 girls and the 4 boys between them as a single entity. So, we have 5 entities (this group of 6 and the remaining 3 boys) to arrange, which can be done in 5 factorial (5!) ways.

Step 4: Within this group of 6 (2 girls and 4 boys), they can be arranged in 6 factorial (6!) ways.

Step 5: Therefore, the total number of favorable outcomes is 5! * 6!.

Step 6: The probability is the ratio of the number of favorable outcomes to the total number of outcomes. So, the probability is (5! * 6!) / 9!.

Step 7: Simplify the expression to get the final probability.

Knowee AI · Accepted Answer

Step 1: Total number of students is 7 boys + 2 girls = 9 students.

Step 2: The total number of ways to arrange these 9 students is 9 factorial (9!).

Step 3: For the condition where there are exactly 4 boys between the 2 girls, we can consider the 2 girls and the 4 boys between them as a single entity. So, we have 5 entities (this group of 6 and the remaining 3 boys) to arrange, which can be done in 5 factorial (5!) ways.

Step 4: Within this group of 6 (2 girls and 4 boys), they can be arranged in 6 factorial (6!) ways.

Step 5: Therefore, the total number of favorable outcomes is 5! * 6!.

Step 6: The probability is the ratio of the number of favorable outcomes to the total number of outcomes. So, the probability is (5! * 6!) / 9!.

Step 7: Simplify the expression to get the final probability.

1 point7 boys and 2 girls are to be placed next to each other in the school ground for morning assembly. What is the probability that there are exactly 4 boys between the 2 girls?

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