Question

Four band members, Harry, Isabel, Jose, and Karen, are all boarding a bus to attend a concert. In each arrangement below, the first initial of each person’s name represents that person’s position as he or she boards the bus: first, second, third, and fourth.

If we know that Karen boards the bus first, which shows the possible outcomes for this event?

KHIJ
KHIJ, KHJI
KHIJ, KHJI, KJHI, KJIH
KHIJ, KHJI, KJHI, KJIH, KIHJ, KIJH

Answer 1

Fixing Karen first leaves H, I, J to arrange in the remaining three spots: 3! = 6 orders. They are

KHIJ, KHJI, KJHI, KJIH, KIHJ, KIJH.

So the fourth choice (the list of six) is correct.