Question

gebra i b-cr
pre-test complete
time remain
57:36
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?
○ khij
○ khij, khji
○ khij, khji, kjhi, kjih
○ khij, khji, kjhi, kjih, kihj, kijh

Explanation:

Step1: Fix first position as K

Karen boards first, so all outcomes start with K.

Step2: List permutations of H,I,J

We need all unique orderings of Harry (H), Isabel (I), Jose (J) for positions 2-4. The permutations of 3 distinct items are: HIJ, HJI, IHJ, IJH, JHI, JIH.

Step3: Attach K to each permutation

Combine K with each permutation: KHIJ, KHJI, KIHJ, KIJH, KJHI, KJIH.

Answer:

KHIJ, KHJI, KJHI, KJIH, KIHJ, KIJH