In how many ways can a photographer at a wedding arrange six people in a row, including the bride and groom, if a) the bride must be next to the groom? b) the bride is not next to the groom? c) the bride is positioned somewhere to the left of the groom?

Answer: a) 240, b) 480, c) 360Step-by-step explanation:Since we have given that Number of people = 6Number of bride and groom = 2So, remaining people = 6-2 = 4So, using the fundamental theorem of counting remaining people can be arranged in [tex]4!=4\times 3\times 2\times 1=24[/tex]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=10So,  a) the bride must be next to the groom?Number of ways = [tex]24\times 10=240[/tex]b) the bride is not next to the groom? Total number of ways would be [tex]6!=6\times 5\times 4\times 3\times 2=720[/tex]So, Number of ways that the bride is not next to the groom is [tex]720-240=480[/tex] c) the bride is positioned somewhere to the left of the groom?If Groom is in second position, bride has 1 ways to standIf Groom is in third position , bride has 2 ways to standIf Groom is in fourth position, bride has 3 ways to standIf Groom is in fifth position, bride has 4 ways to standIf Groom is in sixth position, bride has 5 ways to stand.So, Number of ways to stand = 1+2+3+4+5=15So, the total number of ways bride is positioned somewhere to the left of the groom is given by[tex]24\times 15=360[/tex]Hence, a) 240, b) 480, c) 360