The combination formula nCr is defined as n! / (r!(n-r)!). For 5C5, we substitute n=5 and r=5, resulting in 5! / (5!(5-5)!). Since 0! is defined as 1, the expression simplifies to 5! / (5! * 1), which equals 1. Intuitively, this represents the number of ways to choose 5 items out of a set of 5, which can only be done in exactly one way.

Probability is expressed as a value between 0 and 1. Given that 40% of the items are dress shirts, the probability of selecting one at random is 40 divided by 100, which equals 0.4. The other percentages provided are extraneous information for this specific calculation.

A set of events is considered collectively exhaustive if at least one of the events must occur. When considering the entire sample space, the collection of all possible outcomes is collectively exhaustive because it covers every potential result of the experiment.

In set theory, two sets are considered non-overlapping or disjoint if they share no common elements. Since an individual cannot be both male and female simultaneously in this classification, the intersection of set A and set B is the empty set. Therefore, they are mutually exclusive or non-overlapping.

A fair coin has two equally likely outcomes: heads and tails. The probability of any single specific outcome is the ratio of the number of favorable outcomes to the total number of possible outcomes. Thus, for heads, the probability is 1 divided by 2, or 1/2.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur or how likely it is that a proposition is true. It is measured on a scale from 0 to 1.

The combination formula, denoted as nCr or C(n, r), calculates the number of ways to select a subset of size 'r' from a larger set of 'n' distinct elements where the order of selection does not matter. The formula is n! divided by the product of r! and (n-r)!, representing the total permutations divided by the arrangements of the subset.

Using the addition rule for probabilities, P(A or B) = P(A) + P(B) - P(A and B). Substituting the given values: 0.6 + 0.7 - 0.4 = 1.3 - 0.4 = 0.9. Therefore, the probability of winning at least one of the two cars is 90%.

In this problem, we are given that the probability of getting a head (P(H)) is twice the probability of getting a tail (P(T)). Mathematically, this can be represented as P(H) = 2*P(T). Since the total probability must add up to 1 (or 100%), we can write the equation as P(H) + P(T) = 1. Now, we can substitute the given equation into this equation: 2*P(T) + P(T) = 1. Combining the terms, we get 3*P(T) = 1. Dividing both sides by 3, we find that P(T) = 1/3. Now that we know P(T), we can find P(H) using the original equation P(H) = 2*P(T), which gives us P(H) = 2*(1/3) = 2/3. Therefore, the probability of getting a head is 2/3.

In probability theory, events are considered 'equally likely' if there is no reason to expect one outcome over another. Since a fair coin has two sides and each side has a 50% chance of landing face up, the outcomes of heads and tails are defined as equally likely events.