You conduct a random experiment in which you toss a coin 10 times. How many possible outcomes with exactly 6 heads are there in this random experiment?6105210

The number of possible outcomes with exactly 6 heads in 10 coin tosses can be calculated using the binomial coefficient, which is a term from combinatorics used in probability theory and statistics.

The binomial coefficient is calculated as follows:

C(n, k) = n! / [k!(n-k)!]

where:

• n is the total number of trials (in this case, 10 coin tosses),
• k is the total number of "successes" (in this case, 6 heads),
• "!" denotes factorial, which is the product of all positive integers up to that number.

So, to calculate the number of possible outcomes with exactly 6 heads in 10 coin tosses, we substitute n = 10 and k = 6 into the formula:

C(10, 6) = 10! / [6!(10-6)!] = 10! / [6!4!] = (10987654321) / [(654321)(4321)] = (10987) / (4321) = 210

So, there are 210 possible outcomes with exactly 6 heads in 10 coin tosses.