Final answer:
The number of ways an unbiased coin can land tails exactly 8 times or exactly 2 times when tossed 14 times is found by summing the binomial coefficients (14 choose 8) and (14 choose 2).
Step-by-step explanation:
The question asks about the number of ways an unbiased coin can land tails exactly 8 times or exactly 2 times when tossed 14 times. This is a typical problem of binomial distribution, which falls under the subject of probability in mathematics.
To calculate the number of ways to get exactly 8 tails, we use the binomial coefficient (14 choose 8), which is calculated as 14!/(8!(14-8)!). Similarly, to calculate the number of ways to get exactly 2 tails, we use the binomial coefficient (14 choose 2), which is calculated as 14!/(2!(14-2)!).
The total number of ways the coin can land tails either exactly 8 times or exactly 2 times is the sum of these two binomial coefficients. Therefore, the answer is calculated by adding the result of (14 choose 8) and (14 choose 2).