Question

4. John, Jim, Jay, and Jack have formed a band consisting of 4 instruments. If each of the boys can play all 4 instruments, how many different arrangements are possible? What if John and Jim can play all 4 instruments, but Jay and Jack can each play only piano and drums?

Answer 1

The first part is correct! → There are 4 distinct instruments to distribute to 4 distinct people. And there are 4!=24 distinct ways of doing this.

For the second part. → Jay and Jack can only play 2 instruments, therefore we have 2 instruments for 2 people, and the distribution for these guys can be made in 2!=2 distinct ways.

Then, note that all that is left are 2 distinct instruments for 2 people. So there is an additional 2 distinct ways of doing this distribution for these other guys.

By the product rule, in total, we can do 4 distinct distribution in this condition.

Explanation:

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