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?
Correct 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:
Related math problems and questions:
- Sitting 6612
Seven boys are sitting next to each other in the cinema. How many ways can they sit on the seats if the boys want to sit next to each other? - Together 70124
Twins Ela and Nela came to the cinema together with their friend Hela. Only the first 10 seats in the third row are free. How many ways can they be seated if the twins want to sit next to each other, with Nela always to Ela's left and Hel right next to on - Twins with friend The twins Danka and Janka went to the cinema with their friend Betka. Only six seats in the second row were available in the cinema. The twins want to sit next to each other. Danka is always to the right of Janka, and Betka is near one of them. How many m
- Children 82437
If 3 boys were added to the eighth grade, 50% of the class would be boys. If, on the other hand, 3 girls were added, they would make up 7/12 classes. How many children are there in the class? - 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 chair between them if people choose their place entirely randomly? - How many 31 How many ways can a teacher select a group of 3 students to sit in the front row if the class has 13 students?
- Ninth-grade 5446
When the ninth-grade boys and girls said goodbye at the end of the school year, they each gave each other their photos. It was a total of 552 images. How many farewells were there? - Left-handed 2571
Eva, Lucia, Barbora, Ivana, and Slávka are good friends, so they always want to sit at one long table next to each other in biology class. How many ways can they sit if Slavka is left-handed and, therefore, always wants to sit on the left side of the tabl - Children
The group has 42 children. There are four more boys than girls. How many boys and girls are in the group? - Competition 69474
There are ten girls and seven boys in the dance group. Only one mixed couple is to go to the competition. How many are all possible pairs from which we can choose a pair for the competition? - Classmates 18173
Classmates Anka, Bea, Villa, and Danka can sit next to each other on the bus. What and how many ways can they sit down? - Pears and oranges
There are three times as many pears as oranges. If a group of children receives five oranges each, no oranges will be left over. If the same group of children receives eight pears each, there will be 21 pears left over. How many children and oranges are t - Probability 41071
Six boys and nine girls played in the school group. What probability will they point to the boy when they are reproached? - Veronika 59563
There were five girls in the group. Their names were Veronika, Terezka J., Terezka G., Timea and Ema. Ema was wrong, so they fired her. How many are left? - The ratio 14 The ratio of boys to girls is 8:7. If there are 40 boys, how many girls are there in the class?
- Children 7393
The average age of the children in the group is 14 years. There are four times more boys than girls in the group. The average age of the girls in the group is 12 years. What is the average age of boys? - Students 20003
The class's ratio of boys to girls is 5:7. There are ten boys. How many students are in the class?
