COUNT THE POSSIBILITIES
Colour Probability: Counting Suited Hands
Colour has 1,096 standard three-card hands, approximately 4.9593 percent of the 22,100-hand sample space. First count 286 three-card choices within each suit, then multiply by four. Remove the 48 suited sequences because they occupy the pure-sequence category. The remaining suited, separated-rank hands form the colour category used throughout the Hub.
The rule, precisely
Colour has 1,096 standard three-card hands, approximately 4.9593 percent of the 22,100-hand sample space. First count 286 three-card choices within each suit, then multiply by four. Remove the 48 suited sequences because they occupy the pure-sequence category. The remaining suited, separated-rank hands form the colour category used throughout the Hub.
One suit contains thirteen ranks, so it supports 13 choose 3 = 286 unordered triples. Four suits therefore supply 1,144 suited hands in total. Twelve rank triples in each suit are sequences, giving 48 pure sequences across the pack.
The subtraction is a category partition, rather than a change to the cards. A pure sequence is suited but receives the more specific category. This distinction is essential when category frequencies are expected to sum to the full sample space.
Original Practice Hand
The first hand is a colour and the second is a pure sequence. Both are suited. The counting exercise asks why only the first belongs in the colour-only count. Keep the stated worksheet assumptions beside the cards and record the specific property that supports the worked explanation.
Work through the cards
Count the suited triples within a single suit as 13 × 12 × 11 divided by six, giving 286. Multiply by four suits to obtain 1,144 suited triples across the pack. Keep the stated worksheet assumptions beside the cards and record the specific property that supports the worked explanation.
Count the suited triples within a single suit as 13 × 12 × 11 divided by six, giving 286.
Multiply by four suits to obtain 1,144 suited triples across the pack.
Identify twelve suited rank sequences per suit. Remove 4 × 12 = 48 hands assigned to pure sequence.
Use 1,144 − 48 = 1,096 as the colour-only numerator and divide by 22,100.
Result and next variation
The colour-only fraction is 1,096/22,100, approximately 4.9593%. The broader suited-hand fraction uses 1,144 as its numerator and answers a different question. Keep the stated worksheet assumptions beside the cards and record the specific property that supports the worked explanation. The following steps make that reasoning reproducible for independent study.
Compare a worksheet labelled “any suited hand” with one labelled “colour category”. Write their numerators side by side. This small wording check helps keep statistical questions aligned with the categories actually used in the lesson.
Sources and editorial method
The source note separates published card-rule conventions from the Hub’s own worked examples and mathematical enumeration. Read the declared profile when a convention affects a comparison. Exact cards and calculation steps make the original analysis reproducible, while the editorial policy explains authorship, review scope and the method used to maintain each learning page.
Study convention: The Hub study profile uses one 52-card pack, six standard categories and suit-neutral comparisons. It places A-K-Q above A-2-3, then K-Q-J down to 4-3-2. Practice points count complete explanations within the current page. Read the named convention beside every worked comparison and keep rummy transfer lessons within their own rule system.
Rule reference: Teen Patti rule reference. The Teen Patti reference uses an A-2-3-first ordering; this worksheet uses the declared Hub order. Analysis: fixed teaching deal GH-16; review method by Teen Patti Games Hub Editorial Desk.