Question

Find the number of seating arrangements with all women seated together.

Answer 1

The problem is about finding the number of different seating arrangements where all women are seated together, which is a combinatorics and permutation problem in mathematics.

Step-by-step explanation:

The student is asking about seating arrangements where all women are seated together. In mathematics, this type of problem is related to combinatorics and permutation.

To solve this, treat all the women as one unit and then multiply the number of arrangements of this unit with the number of ways of arranging the women within this unit.

If there are 45 women, first treat them as a single unit which can be arranged in 1 way, and then arrange the 45 women among themselves which can be done in 45! ways.

Thus, there is a total of 1 × 45! different seating arrangements where all women are seated together.

Answer 2

The total number of seating arrangements where all women are seated together is 4, which represents the number of ways the women can be arranged among themselves within the larger arrangement of individuals.

Step-by-step explanation:

In this scenario, let's consider all the women as a single entity. Therefore, there are 4 ways to arrange these women among themselves. Within this "group" of women, their individual positions can be rearranged among themselves in 4 ways. Thus, the total number of seating arrangements with all women seated together is 4.

Now, breaking it down mathematically, let's denote the group of women as a single entity. So, the number of arrangements within this "group" is 4 (as there are 4 women). Then, considering the "group" as one unit, it combines with the remaining men and other elements. The total number of elements now is 5 (the "group" of women and the 5 other individuals). This results in 5! ways to arrange these 5 entitie. However, within the "group" of women, there are 4 arrangements. Hence, to find the total arrangements, we need to multiply 5 by 4 to get the correct number of seating arrangements with all women together.

Therefore, the total number of seating arrangements where all women are seated together is 4, which represents the number of ways the women can be arranged among themselves within the larger arrangement of individuals.