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?\n○ khij\n○ khij, khji\n○ khij, khji, kjhi, kjih\n○ 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?\n○ khij\n○ khij, khji\n○ khij, khji, kjhi, kjih\n○ khij, khji, kjhi, kjih, kihj, kijh

Answer

Explanation:

Step1: Fix Karen's position

Since Karen boards first, her initial 'K' is fixed at the first - position.

Step2: Find permutations of remaining 3

We need to find the permutations of the remaining three initials (H for Harry, I for Isabel, J for Jose). The number of permutations of (n) distinct objects is (n!). Here (n = 3), and (3!=3\times2\times 1=6). The 6 permutations of H, I, J are HIJ, HJI, IHJ, IJH, JHI, JIH. Combining with K at the first - position, the possible outcomes are KHIJ, KHJI, KIHJ, KIJH, KJHI, KJIH.

Answer:

KHIJ, KHJI, KJHI, KJIH, KIHJ, KIJH