Step 1: Understanding the Question:
The basic strength of methyl-substituted amines in aqueous solution is determined by the combined effects of inductive effect (\( +I \)), solvation effect (hydrogen bonding with water), and steric hindrance.
Step 2: Detailed Explanation:
1. Inductive effect: Basic strength should increase with the number of methyl groups: \( 3^{\circ}>2^{\circ}>1^{\circ}>NH_{3} \).
2. Solvation effect: Basic strength increases with the ability to form H-bonds with water: \( NH_{3}>1^{\circ}>2^{\circ}>3^{\circ} \).
3. Steric hindrance: Higher for tertiary amines, making the lone pair less available for donation.
For methyl groups, the experimental order in water is:
Secondary (\( 2^{\circ} \)) > Primary (\( 1^{\circ} \)) > Tertiary (\( 3^{\circ} \)).
Order: \( (CH_{3})_{2}NH>CH_{3}NH_{2}>(CH_{3})_{3}N \).
Step 3: Final Answer:
The correct decreasing order is (CH$_{3}$)$_{2}$NH > CH$_{3}$NH$_{2}$ > (CH$_{3}$)$_{3}$ N.