Simplify 9C4.
- 126 ***
- 15,120
- 5
- 3,024
9C4=9!/((9-4)!4!)
Use your calculator to work that out.
and yes, you are correct.
To simplify 9C4, we can use the formula for combinations:
C(n, r) = n! / (r! * (n - r)!)
In this case, n = 9 and r = 4.
Plugging in the values:
9C4 = 9! / (4! * (9 - 4)!) = 9! / (4! * 5!)
Now, let's calculate the factorial values:
9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
4! = 4 * 3 * 2 * 1
5! = 5 * 4 * 3 * 2 * 1
Substituting these values back into the equation:
9C4 = (9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (4 * 3 * 2 * 1 * (5 * 4 * 3 * 2 * 1))
A lot of terms cancel out:
9C4 = (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1)
Now, let's do the calculations:
9C4 = (3024) / (24) = 126
Therefore, the simplified value of 9C4 is 126.
To simplify the expression 9C4, we need to find the number of ways to choose 4 items from a set of 9 items.
The formula for calculating combinations is given by the formula: nCk = n! / (k! * (n-k)!), where n is the total number of items and k is the number of items being chosen.
In this case, n = 9 (since we are choosing from a set of 9 items) and k = 4 (since we want to choose 4 items).
Substituting the values into the formula, we have: 9C4 = 9! / (4! * (9-4)!)
Now we need to calculate the factorials.
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
Plugging these values back into the formula, we get: 9C4 = 362,880 / (24 * 120)
Simplifying the denominator, we have: 24 * 120 = 2,880
Therefore, 9C4 = 362,880 / 2,880 = 126.
So the simplified answer for 9C4 is 126.