four band members, harry, isabel, jose, and karen, are all boarding a bus to attend a concert. in each…

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 persons name represents that persons 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?\no khij\no khij, khji\no khij, khji, kjhi, kjih\no khij, khji, kjhi, kjih, kihj, kijh

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 persons name represents that persons 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?\no khij\no khij, khji\no khij, khji, kjhi, kjih\no khij, khji, kjhi, kjih, kihj, kijh

Answer

Explanation:

Step1: Fix Karen's position

Since Karen boards first, we only need to arrange Harry (H), Isabel (I), and Jose (J) in the remaining 3 positions.

Step2: Calculate number of arrangements

The number of permutations of 3 distinct objects is given by (n!=n\times(n - 1)\times\cdots\times1). Here (n = 3), so (3!=3\times2\times1=6). The possible arrangements of H, I, J are HIJ, HJI, JHI, JIH, IHJ, IJH. Combining with Karen (K) in the first - position, we get KHIJ, KHJI, KJHI, KJIH, KIHJ, KIJH.

Answer:

KHIJ, KHJI, KJHI, KJIH, KIHJ, KIJH