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Explanations for this problem are greatly appreciated! In Candy Lane Middle School there are 20 s...

Explanations for this problem are greatly appreciated!

In Candy Lane Middle School there are 20 students including Billy, Joe, and Amanda that need to be put in school clubs. Each student is to be called one at a time to join a club. There are a total of 5 clubs students can join. How many ways are there to distribute all of the 20 students into clubs so that Billy, Joe, and Amanda are in the same club together?

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Answer #1

Consider Billy, Joe and Amanda as one person  

Consider they are in the same club together.

So there remains a total of 20-3=17 students

Now Billy Joe Amanda are considered as one person. So total of 17+1=18 students to be arranged in 5 clubs.

So total number of required ways:5^18=3814697265625

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