<p>In an Ice cream parlor at South City Mall Kolkata, 4 different varieties of ice creams namely Vanila, Strawberry, Chocolate and Butter Scotch were available. On a particular day it was noticed that each customer buys at least one ice cream and at max 10 ice creams, on further investigation it was noticed that no two customer buys same set of ice creams then find the number of customers visited the ice cream shop on that particular day.</p>
Step-by-Step Solution
Key Concept: Each customer buys a distinct non-empty subset of the 4 ice cream varieties, with the constraint that total quantity per customer is between 1 and 10. The key is recognizing that the problem asks for distinct SETS of ice creams, not quantities—we count subsets of {V, S, C, B}, which is 2^4 - 1 (excluding empty set).
<p><strong>Step 1:</strong> Identify what we're counting: Each customer buys a distinct SET of ice cream varieties from {Vanilla, Strawberry, Chocolate, Butter Scotch}. The constraint 'at least 1 and at max 10' simply means no customer buys the empty set (at least 1) and no impossibility arises with 4 varieties.</p><p><strong>Step 2:</strong> The total number of non-empty subsets of a 4-element set = 2^4 - 1 = 16 - 1 = 15. (We subtract 1 to exclude the empty set, which violates 'at least one ice cream'.)</p><p><strong>Step 3:</strong> Since no two customers buy the same set of ice creams, and there are exactly 15 distinct non-empty sets possible, the number of customers = 15.</p><p><strong>Verification:</strong> Possible sets include: {V}, {S}, {C}, {B}, {V,S}, {V,C}, {V,B}, {S,C}, {S,B}, {C,B}, {V,S,C}, {V,S,B}, {V,C,B}, {S,C,B}, {V,S,C,B} = 15 sets ✓</p><p>∴ <strong>Answer: 15 customers</strong></p>
Correct Answer: 15