A classical music concert is to consist of 5 cello pieces 3

A classical music concert is to consist of 5 cello pieces, 3 choral works, and 3 pieces for piano. In how many ways can the program be arranged if a piano piece must come first?

A. 10,886,400

B. 120,960

C. 3,628,800

D. 39,916,800

Solution

We have total of 11 pieces, divided 5 cello pieces, 3 choral works, and 3 pieces piano
We have condition to fill the first piece with piano piece. First blank could be fill with
3 possible and the remainig 10 pieces can fill with 10*9*8*7*6*5*4*3*2*1 ways

Total No. of arrangements are = 3 * 10*9*8*7*6*5*4*3*2*1 = 10886400

[ANSWER] A. 10886400