There are five girls and five boys at a party. In how many ways can they be seated in a row of six?
To determine the number of ways the girls and boys can be seated in a row of six, we can use the concept of permutations.
First, we need to arrange the five girls. There are 5 girls, so we have 5 choices for the first seat, then 4 choices for the second seat, 3 choices for the third seat, and so on. This can be represented as 5!.
Next, we need to arrange the five boys in the remaining seats. There are 5 boys, and since there is only one seat left, each boy can take that seat. So, there is only 1 way to arrange the boys.
Finally, to find the total number of seating arrangements, we multiply the number of ways the girls can be seated by the number of ways the boys can be seated:
Total number of arrangements = 5! * 1
= 5!
Therefore, there are 5! (which is equal to 5 factorial) ways to seat the girls and boys in a row of six.
10*9*8*7*6*5
or 10!/(10-6)!