School group
There are five girls and seven boys in the group. They sit in a row next to each other. How many options if no two girls sit next to each other?
Final Answer:
Showing 1 comment:
Dr Math
This problem is identical to saying if you have 7 boys in a row, how many ways are their to place 5 girls in that row without having two girls next to each other. you would have 8 locations to choose from.
B B B B B B B
+ B + B + B + B + B + B + B +
Here you have 8 places to arrange the girls and 5 girls. This is the same as 8 choose 5 which equals 56.
Then for each of those 56 arrangements, you can look at every possible arrangement of individual girls, the number of which is 5!
Lastly for each of those unique placement of girls, and unique order of gils, you can take the unique order of boys which would be 7!
In my calculation, the total should be 56 x 5! x 7! = 33868800
B B B B B B B
+ B + B + B + B + B + B + B +
Here you have 8 places to arrange the girls and 5 girls. This is the same as 8 choose 5 which equals 56.
Then for each of those 56 arrangements, you can look at every possible arrangement of individual girls, the number of which is 5!
Lastly for each of those unique placement of girls, and unique order of gils, you can take the unique order of boys which would be 7!
In my calculation, the total should be 56 x 5! x 7! = 33868800
Tips for related online calculators
You need to know the following knowledge to solve this word math problem:
combinatoricsGrade of the word problem
Related math problems and questions:
- Table and chairs
Four people should sit at a table in front of a row of 7 chairs. What is the probability that there will be no empty chairs between them if people randomly choose their place? - Children
The group has 42 children. There are four more boys than girls. How many boys and girls are in the group? - Kids
How many different ways can sit 6 boys and 3 girls in line if girls want to sit on the edge? - Boy selection probability
Six boys and nine girls played in the school group. What probability will they point to the boy when they are reproached? - Peter and Lucy
In a group of 3 boys and 4 girls, two players are drawn to play a game. Among the girls is Lucy, and among the boys is Petr (both are the only ones with that name). The first one drawn will be the captain, the second the helmsman. What is the probability - Dance couple pairs
Ten girls and seven boys are in the dance group. Only one mixed couple is to go to the competition. How many possible pairs can we choose from? - Weekly pair options
There are 13 boys and 17 girls in the class. The weeklies are always either two girls or a boy and a girl. The teacher calculated that she has 357 ways to create a pair of weekly newspapers. However, Anetka did not come to school on Monday morning. How ma
