Q.1.4 - A First Course in Probability

Question

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? 

Step-by-Step Solution

Answer

 The different ways of arrangements are 24.

The ways of arrangement when John and Jim can play all 4 instruments, but Jay and Jack can each play only piano and drums are 4.

Step 1 .Given information

John, Jim, Jay, and Jack k, each of the boys can play all 4 instruments 

We have to find out the number of arrangements if four of them playing different instruments and when John and Jim can play all 4 instruments, but Jay and Jack can each play only piano and drums.

Step 2 . Description of possible arrangements

 If each of the boys plays all instruments, then using different permutations for 4 different instruments, we get there are  $$\begin{gathered} 4! =4\times 3\times 2\times 1 \\ =24 \end{gathered}$$

different arrangements are possible.

 Since Jay and jack play only piano and drums,  then arrangements for them is 2! using different permutations concepts,

John and Jim can play all, but only 2 instruments are left there because of the other two people,  hence the arrangement for them is 2!.

Thus possible arrangement when John and Jim can play all 4 instruments, but Jay and Jack can each play only piano and drums  is $2!\times 2!=4$