6. Combination of 9 pick 6

This seems easy but I am not sure how to set the problem up.

Thanks!

9!/3!6!

C(9,6)

= 9!/(6!3!)
= 362880/(720 x 6)
= 84

you should have a C(n, r) key on you r calculator
sometimes shown as nCr
on mine it is found under the "5" key

so enter
9
nCr
6
=

to get 84

To solve the combination problem of "9 pick 6," you need to determine the number of ways you can choose 6 items from a set of 9 items without regard to their order. Here's how you can set up the problem:

Step 1: Understand the formula used to calculate combinations.
The formula for combinations is given by C(n, r) = n! / ((n-r)! * r!), where n is the total number of items and r is the number of items being chosen.

Step 2: Identify the values for n and r in your problem.
In this case, n represents the total number of items (9) and r represents the number of items to be chosen (6).

Step 3: Plug the values into the formula.
C(9, 6) = 9! / ((9-6)! * 6!)

Step 4: Simplify and solve.
9! is the factorial of 9, which means multiplying all the whole numbers from 1 to 9 together. Similarly, (9-6)! is the factorial of 3 and 6! is the factorial of 6.
So, the equation becomes: C(9, 6) = 9! / (3! * 6!)

Step 5: Calculate the factorials.
9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
3! = 3 * 2 * 1
6! = 6 * 5 * 4 * 3 * 2 * 1

Step 6: Substitute the values into the equation.
C(9, 6) = (9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / ((3 * 2 * 1) * (6 * 5 * 4 * 3 * 2 * 1))

Step 7: Simplify and solve.
C(9, 6) = 84

So, the combination of "9 pick 6" is 84, which means there are 84 different ways to choose 6 items from a set of 9 items.