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Combinations are a fundamental concept in probability and statistics that deal with selecting a specific number of items from a larger pool, where the order of selection does not matter. In the context of the problem, we are tasked with selecting 3 cards out of a total of 20. To determine the number of ways to do this, we utilize the combination formula:
\[\binom{n}{r} = \frac{n!}{r!(n-r)!}\]
This formula represents the number of ways to choose \(r\) items from a total of \(n\) without regard to the sequence. For the exercise given, it means we plug in 20 for \(n\) and 3 for \(r\). By calculating \(\binom{20}{3} = 1140\), it shows that there are 1140 possible outcomes for selecting any 3 cards from the 20 available.
Thus, understanding combinations helps us to assess the total number of configurations without considering the order, which is essential in calculating realistic probabilities.

Permutation and combination are closely related yet distinct concepts in probability theory. Both deal with the arrangement of elements but differ significantly in terms of order importance. Permutations concern situations where order matters, whereas combinations do not.
In our specific problem, after determining the combinations of card selections, we dive into permutations for ordering within those selections. While **combinations** calculate how many groups of cards can be selected, permutations would be relevant if the position (order) of each card within those groups also impacts the result. Since the arrangement 'IIT' needs specific positions filled with specific cards, permutations allow for further discernment.
To draw the word 'IIT', we have to choose the cards correctly, focusing on the constraints that dictate which card must take which position. This is why first using combinations to select the cards and then tailoring the exact order through permutations provides a layered approach to solving such probability puzzles effectively. This step-by-step narrowing focus significantly refines our search for valid outcomes.

Probability theory is the mathematical framework that underlines the principles of predicting the likelihood of events. It revolves around measuring the chance, from 0 to 1, of an event occurring.

• A probability of 0 means the event won't occur.
• A probability of 1 means the event is certain to occur.
• Values between 0 and 1 express varying chances of occurrence.

In the context provided, the probability of forming the word 'IIT' is expressed by comparing favorable outcomes to the total number of possible outcomes. Mathematically, this is given as:
\[P(\text{IIT}) = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} = \frac{450}{1140}\]
Here, 450 represents the specific ways to form the word 'IIT', while 1140 is the total ways to pick any 3 cards. Simplifying this ratio gives a more manageable probability expression, emphasizing the simplicity and elegance of probability theory in assessing likely scenarios.
By systematically identifying both possible outcomes and favorable cases, probability theory provides a structured approach to analyzing such random processes and investigating the various likelihood events within them.