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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?

A=KHIJ
B=KHIJ, KHJI
C=KHIJ, KHJI, KJHI, KJIH
D=KHIJ, KHJI, KJHI, KJIH, KIHJ, KIJH

Verified Answer :

CheyHargrove
DKHIJ KHJI KJHI KJIH KIHJ KIJH
dubeyshailja64

The possible outcomes for the given event are KHIJ, KHJI, KJHI, KJIH, KIHJ, KIJH.

The total outcomes for the given questions can be calculated by the use of permutation.

What is permutation?

A permutation is a mathematical technique that is used to calculate total possible outcomes for arrangement provided that the order of selection of items is not fixed.

The formula to determine permutation is:

\(^nP_{r} = \dfrac{n!}{(n - r)!}\)

where n is the total number of objects and r is the number of objects selected.

For the given question, n will be 3 since K boards the bus first and hence his position is fixed. Therefore H, I, and J can switch positions.

Hence,

\(^nP_{r} = \dfrac{n!}{(n - r)!}\\\\^nP_{r} = \dfrac{3!}{(3 - 2)!}\\\\^nP_{r} = 3 x 2\\\\^nP_{r} = 6\)

Therefore the correct option is D.

Learn more about permutation here:

https://brainly.com/question/14767366

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