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!]
= (10*9*8*7*6*5*4*3*2*1) / [(6*5*4*3*2*1)*(4*3*2*1)]
= (10*9*8*7) / (4*3*2*1)
= 210

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

Question

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!]
         = (10*9*8*7*6*5*4*3*2*1) / [(6*5*4*3*2*1)*(4*3*2*1)]
         = (10*9*8*7) / (4*3*2*1)
         = 210

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

Knowee AI · Accepted Answer

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!]
         = (10*9*8*7*6*5*4*3*2*1) / [(6*5*4*3*2*1)*(4*3*2*1)]
         = (10*9*8*7) / (4*3*2*1)
         = 210

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

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

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