Evaluate the given expression.
C(9,4)
C(9,4) = 9! / [ 4! (5!) ]
= 9 * 8 * 7 * 6 / (4*3*2)
= 3 * 2 * 7 * 3
126
C(9,4) is the combination of choosing 4 items out of a set of 9 items. But you know what they say, when life gives you combinations, make a delicious math salad! So let's get cookin'!
To calculate C(9,4), we can use the combination formula:
C(n,r) = n! / (r!(n-r)!)
Plugging in the values, we have:
C(9,4) = 9! / (4!(9-4)!)
Now, let's do some number crunching. I hope you brought your appetite for math. *wink*
9! (that's the factorial of 9) is equal to 362,880.
4! (the factorial of 4) is just 24.
And 9 - 4 is, well, 5.
So, the equation becomes:
C(9,4) = 362,880 / (24 * 5!)
But wait, we need to find the value of 5! (the factorial of 5) first.
5! = 5 * 4!
= 5 * 4 * 3!
= 5 * 4 * 3 * 2!
= 5 * 4 * 3 * 2 * 1!
= 5 * 4 * 3 * 2 * 1
= 120
Phew, all that multiplication got me dizzy! Now let's go back to our modified equation:
C(9,4) = 362,880 / (24 * 120)
24 * 120 gives us 2,880, and when we divide 362,880 by 2,880, we get:
C(9,4) ≈ 126
So, my dear friend, the value of C(9,4) is approximately 126. Enjoy your math salad, and don't forget to add a sprinkle of humor!
To evaluate the expression C(9,4), we will use the combination formula. The combination formula is given by:
C(n, r) = n! / (r! * (n - r)!)
In this formula, n represents the total number of items and r represents the number of items being chosen.
Let's substitute the values from the given expression into the formula:
C(9, 4) = 9! / (4! * (9 - 4)!)
To simplify, we need to calculate the factorial of 9, 4, and (9 - 4):
9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 362,880
4! = 4 * 3 * 2 * 1 = 24
(9 - 4)! = 5! = 5 * 4 * 3 * 2 * 1 = 120
Now, substitute the values into the formula:
C(9, 4) = 362,880 / (24 * 120)
Simplify the denominator:
C(9, 4) = 362,880 / 2,880
Perform the division to find the final value:
C(9, 4) ≈ 126
Therefore, C(9,4) is approximately equal to 126.
To evaluate the expression C(9,4), we need to use the formula for combinations. The formula for combinations, also represented by C(n, r), is:
C(n, r) = n! / (r! * (n-r)!)
where "n" represents the total number of items or choices, and "r" represents the number of items or choices being selected.
In this case, C(9,4) means we are selecting 4 items from a total of 9 items.
To calculate C(9,4), we need to substitute the values into the formula:
C(9,4) = 9! / (4! * (9-4)!)
Now, let's evaluate the factorials:
9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
4! = 4 * 3 * 2 * 1
(9-4)! = 5! = 5 * 4 * 3 * 2 * 1
Substituting the values:
C(9,4) = (9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (4 * 3 * 2 * 1 * 5 * 4 * 3 * 2 * 1)
Simplifying further:
C(9,4) = (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1)
Cancelling out the common terms:
C(9,4) = (9 * 8 * 7 * 6) / (4!)
Calculating the remaining multiplication:
C(9,4) = 3024 / 24
C(9,4) = 126
Therefore, C(9,4) = 126.