#first course in probability #sheldon_ross 8th edition Chapter 1 ,question 4

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?

Comments

John and Jim can play all 4 instruments --->  4 x 3  = 12 ways  

The other two can play only two instruments (piano and drum) ---> 2! = 2 ways

Adding all the possibilities gives 14 ways

---

plz explain 1st one

---

All four of them can play all four instruments. Thus this is just 4!

Answer 1

let the characters in the question are j1,j2,j3,j4.

J1 has 4 choices to any of the instrument i.e 4 ways, now lets J1 choose instrument Ins1.
so, J2 only left with 3 choices, then J2 also chosen, J3 left only two choices and J4 with only Inst. which no one chose.

i.e no. of ways J1 can choose * J2 can choose * J3 can Choose * J4 can choose = the total number of ways.
4*3*2*1=4!

2.
J4 & J3 can only play drum and piano so J4 has two choices either choose drum or piano other one is given to J3, so together 2 ways and remaining two instruments are selected among J1 & J2 also 2 ways. Total 2*2=4 ways.