Answer to Question #203381 in Statistics and Probability for Max

Question

A musical director wants a line across the stage consisting of 25 people playing the following instruments: 8 trumpets, 7 clarinets, 5 flutes, 4 trombones and 1 drum. He has to choose the musicians from a group of 25 peoples. Each person in the group can play any of the instruments mentioned. The director is only concerned with the arrangement of the instruments, that is, he views all the players as identical.

a)How many arrangements are possible?

b)How many arrangements are possible if the director decides to put the drum in the centre, the trumpets and trombones on the left and the clarinets and flutes on the right?

Answer 1

a)

$N=C^8_{25}\cdot C^7_{17}\cdot C^5_{10}\cdot C^4_{5}=1081575\cdot19448\cdot252\cdot5=26,503,432,956,000$ ways

b)

$N=C^8_{12}\cdot C^7_{12}=495\cdot 792=392040$