In how many ways can the six students be introduced?

gmattesttaker2 wrote:Hello,

Can you please assist with this:

A teacher has to decide in which order duets P, Q, and R will play at a school concert as
well as the order in which he will introduce each of the two students that make up a duet
before each duet plays. In how many ways can the six students be introduced?

(A) 12
(B) 24
(C) 36
(D) 48
(E) 60

OA: D


Thanks a lot,
Sri

Let the duets be played by the following pairs:
Duet P --> A and B.
Duet Q--> C and D.
Duet R --> E and F.

There are a total of 6 positions in the concert:
PP-QQ-RR (not necessarily in this order).

Number of options for A = 6. (Any of the 6 positions in the concert.)
Number of options for B = 1. (Once A has been placed, B must be occupy the remaining position in duet P.)
Number of options for C = 4. (Any of the 4 remaining positions in the concert.)
Number of options for D = 1. (Once C has been placed, D must occupy the remaining position in duet Q.)
Number of options for E = 2. (Either of the 2 remaining positions in the concert.).
Number of options for F = 1. (Only one position left.)
To combine these options, we multiply:
6*1*4*1*2*1 = 48.

The correct answer is D.