evaluate 8c5
(8*7*6*5*4) / (1*2*3*4*5)
Note that it is equal to
8!/(5!3!)
Note also that 8C5 = 8C3
choosing 5 things is the same as choosing 3 things to exclude.
To evaluate 8C5, we need to use the binomial coefficient formula, also known as the combination formula. The formula for evaluating combinations is:
nCr = n! / (r!(n-r)!)
In this case, n = 8 and r = 5. Let's substitute these values into the formula:
8C5 = 8! / (5!(8-5)!)
Next, let's simplify the equation by calculating the factorials:
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320
5! = 5 x 4 x 3 x 2 x 1 = 120
3! = 3 x 2 x 1 = 6
Now, let's substitute the calculated factorials back into the equation:
8C5 = 40,320 / (120 x 6)
Next, let's simplify the denominator:
120 x 6 = 720
Now, let's substitute the simplified denominator back into the equation:
8C5 = 40,320 / 720
Finally, let's divide to get the answer:
8C5 = 56
Therefore, 8C5 is equal to 56.
To evaluate 8c5, you need to calculate the binomial coefficient or "8 choose 5." The binomial coefficient represents the number of ways to choose k elements from a set of n elements, and is calculated using the formula:
nCk = n! / (k!(n-k)!)
where "n!" represents the factorial of n, which is the product of all positive integers less than or equal to n.
Using this formula, we can calculate 8c5 as follows:
8c5 = 8! / (5!(8-5)!)
= 8! / (5!3!)
Now, let's calculate the factorial values:
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
5! = 5 x 4 x 3 x 2 x 1
3! = 3 x 2 x 1
Substituting these values:
8c5 = (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / ((5 x 4 x 3 x 2 x 1) x (3 x 2 x 1))
Next, we can simplify the expression:
8c5 = (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (5 x 4 x 3 x 2 x 1 x 3 x 2 x 1)
= (8 x 7 x 6) / (3 x 2 x 1)
Calculating the numerator and denominator:
8c5 = 336 / 6
= 56
Therefore, 8c5 is equal to 56.