Question: The six members of the student council...

Question

1.The six members of the student council

executive are lined up for a yearbook photo.

c) In how many ways could this be done if

the president and vice president must sit

together in the middle of the group?

Answer 1

ABPVCD

ABPVDC

ACPVBD

ACPVDB

ADPVCB

ADPVBC

6 more with VP instead of PV

2x6 = 12 ways with A on left

BAPVCD

BAPVDC

BCPVAD

BCPVDA

BDPVAC

BDPVCA

6 more with VP instead of PV

2x6 = 12 ways with B on left

CAPVBD

CAPVDB

CBPVAD

CBPVDA

CDPVAB

CDPVBA

6 more with VP instead of PV

6x2 = 12 ways with C on left

another 12 with D 1st on the left

that's 12 x 4 = 48 different ways

2 x 4! = 2(4x3x2x1) = 2(24) = 48