(P) 1-Bromo-2-ethylpentane via S${}_N$2. The leaving group is on a primary carbon; the stereocentre at C-2 is not the site of substitution. Hence its configuration is preserved: retention of configuration at the existing stereocentre. Match $\to$ (2).

(Q) 2-Bromopentane via S${}_N$2. Substitution occurs at the stereocentre; bimolecular back-side attack causes Walden inversion. Inversion of configuration. Match $\to$ (1).

(R) 3-Bromo-3-methylhexane via S${}_N$1. Ionisation generates a planar tertiary carbocation at the stereocentre. Hydroxide attacks both faces equally, giving a racemic mixture: mixture of enantiomers. Match $\to$ (3).

(S) S${}_N$1 on a substrate with two stereocentres. Ionisation at one stereocentre yields a planar carbocation; hydroxide attacks either face. Because the second (unchanged) stereocentre remains intact, the two product alcohols differ at only one stereocentre, giving a pair of diastereomers. Match $\to$ (5).

Mapping: P $\to$ 2, Q $\to$ 1, R $\to$ 3, S $\to$ 5. Answer: (B).