Title: 2018 Slot 2 Quant - Indian Game Problem Solution
Problem Statement (Hypothetical Example):
In a traditional Indian game, players draw 3 cards from a deck of 52 cards. The deck contains 13 cards each of four suits: Spades, Hearts, Diamonds, and Clubs. A "lucky hand" is defined as one that includes exactly two cards of the same suit and one card of a different suit. What is the probability of drawing a lucky hand?
Solution:
Total Possible Hands:
The number of ways to choose 3 cards from 52 is calculated using combinations:
[
\text{Total} = \binom{52}{3} = \frac{52 \times 51 \times 50}{3 \times 2 \times 1} = 22100
]
Favorable Outcomes (Lucky Hands):
Step 1: Choose the suit for the two identical cards.
There are 4 suits, so:
[
\binom{4}{1} = 4
]
Step 2: Choose 2 cards from the selected suit.
Each suit has 13 cards:
[
\binom{13}{2} = \frac{13 \times 12}{2} = 78
]
Step 3: Choose a different suit for the third card and pick 1 card from it.
Choose 3 remaining suits:
[
\binom{3}{1} = 3
]
Pick 1 card from the chosen suit:
[
\binom{13}{1} = 13
]
Total Favorable:
[
4 \times 78 \times 3 \times 13 = 4 \times 78 \times 39 = 12168
]
Probability Calculation:
[
\text{Probability} = \frac{\text{Favorable}}{\text{Total}} = \frac{12168}{22100} \approx 0.5516 , \text{(or 55.16%)}
]
Key Takeaways:
Use combinatorial logic to break down choices systematically.
Ensure no overlap in suits (third card must be from a different suit).
Simplify calculations by grouping steps (e.g., suits and card selections).
Answer: The probability of drawing a lucky hand is approximately 55.16%.
This solution aligns with common quantitative reasoning patterns in Indian standardized tests (e.g., CAT), emphasizing combinatorial probability and structured problem-solving.
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