It is required to seat 5 men and 4 women in a row so that the women occupy the Even place. How many arrangements are possible?
M W M W M W M W M
This means that 5 men will have 5 different places to choose from, and women will have four.
Men's choices = 5*4*3*2*1
Women's choices = 4*3*2*1
They can be arranged independently, so the product of the number of choices of each gender will give the total number of arrangements.
To calculate the number of arrangements, we can use the concept of permutations.
Since there are 5 men and 4 women, we have a total of 9 people. To make sure the women occupy the even places, we can consider the even places as fixed positions for the women, and then arrange the men and women separately.
First, let's arrange the women in the even positions. Since there are 4 women and 5 even positions, we have 5 choices for the woman in the first even place, 4 choices for the second even place, 3 choices for the third even place, and 2 choices for the fourth even place.
So, the number of arrangements for the women in the even places is 5 x 4 x 3 x 2 = 120.
Now, let's arrange the men in the remaining odd places. Since there are 5 men and 5 odd positions, we have 5 choices for the man in the first odd place, 4 choices for the second odd place, 3 choices for the third odd place, 2 choices for the fourth odd place, and 1 choice for the fifth odd place.
So, the number of arrangements for the men in the odd places is 5 x 4 x 3 x 2 x 1 = 120.
Finally, we can calculate the total number of arrangements by multiplying the number of arrangements for the women and the number of arrangements for the men: 120 x 120 = 14,400.
Therefore, there are 14,400 possible arrangements to seat the 5 men and 4 women in a row so that the women occupy the even places.