Question

probability and statistics
miriam is visiting five friends in her neighborhood, louise, mike, nicole, oscar, and pascal. in each arrangement, the first
initial of each persons name represents that persons position as he or she is visited by miriam.
which shows all the outcomes for this event if she visits with nicole first and louise last?

Explanation:

Step1: Determine fixed positions

Since Nicole (N) is first and Louise (L) is last, we only need to arrange Mike (M), Oscar (O), and Pascal (P) in the middle three positions.

Step2: Calculate permutations of middle three

The number of permutations of \(n\) distinct objects is \(n!\). Here \(n = 3\), so \(3! = 3\times2\times 1=6\) permutations.
The permutations of M, O, P are:

• When the second - third - fourth positions are M - O - P: NMOPL
• When the second - third - fourth positions are M - P - O: NMPOL
• When the second - third - fourth positions are O - M - P: NOMPL
• When the second - third - fourth positions are O - P - M: NOPML
• When the second - third - fourth positions are P - M - O: NP MOL
• When the second - third - fourth positions are P - O - M: NPOML

Answer:

NMOPL, NMPOL, NOPML, NOMPL, NPMOL, NPOML (corresponding to the third option in the given choices)