Five different books (P, Q, R, S, T) are to be arranged on a shelf. The books R and S are to be arranged first and secon...

Question

Five different books (P, Q, R, S, T) are to be arranged on a shelf. The books R and S are to be arranged first and second, respectively from the right side of the shelf. The number of different orders in which P, Q and T may be arranged is ______.
A. 2
B. 6
C. 12
D. 120

Accepted Answer

6 The shelf has 5 positions. R occupies position 5 (rightmost) and S occupies position 4 (second from right). These two books are fixed. The remaining 3 books — P, Q, T — can fill the 3 remaining positions (positions 1, 2, 3 from the left) in any order. The number of ways to arrange 3 distinct books in 3 positions is 3! = 6.

Five different books (P, Q, R, S, T) are to be arranged on a shelf. The books R and S are to be arranged first and second, respectively from the right side of the shelf. The number of different orders in which P, Q and T may be arranged is ______. A. 2 B. 6 C. 12 D. 120