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irina1246 [14]
3 years ago
5

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 mus

t 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?
Mathematics
1 answer:
ELEN [110]3 years ago
5 0

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

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

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

So, Number of ways that the bride is not next to the groom is

720-240=480

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

Hence, a) 240, b) 480, c) 360

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