3 boys, 2 girls and a puppy sit at a round table. In how many ways can they be arranged if the puppy is to be seated between any 2 boys?
Case 1: The girls sit together
No. of ways=(4-1)!(2!)=12
Case2: The girls are seperated
No. of ways=(5-1)!=24
Total no. of ways=12+24=36
Since there are boys and seats the number of arrangements is : , if you don't take in consideration who is on the left hand side from the puppy and who is on the right hand side from the puppy .
So , to get total number of ways you have to double number :
Now,in each arrangement there are more free seats and boy and girls...so you have number of ways in which they can sit .
Finally , to get total number of arrangements you have to multiply by
Hello, Punch!
3 boys, 2 girls and a puppy sit at a round table.
In how many ways can they be arranged
if the puppy is to be seated between any 2 boys?
Assume there are six chairs around the table.
The puppy can sit anywhere (it doesn't matter).
There are 3 choices for the boy on its left.
There are 2 choices for the boy on its right.
The other 3 people (1 boy, 2 girls) can be seated in 3! ways.
Therefore: . ways.