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# counting 'basics'

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At a wedding, the bride and groom want to take a picture in a line with their 5 other friends.
However, the bride and groom have requested that they be placed next to each other. How
many ways can they line up for the picture?

Aug 21, 2023

#2
+126978
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The bride and groom  can  be  thought  of  as one  unit  which can occupy any six positions and  for  each of these they can  be  arranged  in 2 ways  and  for  each of these arrangements the other 5 can  be arranged  in  5! ways...so....

6 * 2 * 5!  =    12 *  120  =    1440  ways

Aug 22, 2023

#1
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We can think of the bride and groom as a single unit, so there are 6 people to line up. We can do this in 6! ways. However, the bride and groom can switch places, so we need to divide by 2. Therefore, the total number of ways to line up is 6!/2​=360​.

Another way to solve this problem is to think of the bride and groom as being in the same position. Then there are 5 people to line up, which can be done in 5! ways. But since the bride and groom can switch places, we need to multiply by 2. This gives us the same answer of 6!/2​=360.

Aug 21, 2023
#2
+126978
+1

The bride and groom  can  be  thought  of  as one  unit  which can occupy any six positions and  for  each of these they can  be  arranged  in 2 ways  and  for  each of these arrangements the other 5 can  be arranged  in  5! ways...so....

6 * 2 * 5!  =    12 *  120  =    1440  ways

CPhill Aug 22, 2023