Answer: a) 240, b) 480, c) 360
Step-by-step explanation:
Since we have given that
Number of people = 6
Number of bride and groom = 2
So, remaining people = 6-2 = 4
So, using the fundamental theorem of counting
remaining people can be arranged in
![4!=4\times 3\times 2\times 1=24](https://tex.z-dn.net/?f=4%21%3D4%5Ctimes%203%5Ctimes%202%5Ctimes%201%3D24)
Since bride has 5 positions to stand and grooms too has 5 positions to stand.
so, Number of positions for both bride and groom = 5+5=10
So, a) the bride must be next to the groom?
Number of ways = ![24\times 10=240](https://tex.z-dn.net/?f=24%5Ctimes%2010%3D240)
b) the bride is not next to the groom?
Total number of ways would be
![6!=6\times 5\times 4\times 3\times 2=720](https://tex.z-dn.net/?f=6%21%3D6%5Ctimes%205%5Ctimes%204%5Ctimes%203%5Ctimes%202%3D720)
So, Number of ways that the bride is not next to the groom is
![720-240=480](https://tex.z-dn.net/?f=720-240%3D480)
c) the bride is positioned somewhere to the left of the groom?
If Groom is in second position, bride has 1 ways to stand
If Groom is in third position , bride has 2 ways to stand
If Groom is in fourth position, bride has 3 ways to stand
If Groom is in fifth position, bride has 4 ways to stand
If Groom is in sixth position, bride has 5 ways to stand.
So, Number of ways to stand = 1+2+3+4+5=15
So, the total number of ways bride is positioned somewhere to the left of the groom is given by
![24\times 15=360](https://tex.z-dn.net/?f=24%5Ctimes%2015%3D360)
Hence, a) 240, b) 480, c) 360