Which number is larger in each of the following pairs
a.)C(9,3), C (10,2)
b.)C(12,4), C (18,3)
c.)C(9,3), 6!
d.)3^5,5!
To find the larger number in each of the following pairs, we need to understand the calculation of these values.
a.) C(9,3), C(10,2)
C(n, r) represents the number of combinations, also known as binomial coefficients, of selecting r elements from a set of n elements. The formula to calculate C(n, r) is:
C(n, r) = n! / (r! * (n - r)!)
In this case, we have:
C(9,3) = 9! / (3! * (9 - 3)!)
C(10,2) = 10! / (2! * (10 - 2)!)
To find which number is larger, we can compute these values using factorials and compare them.
b.) C(12,4), C(18,3)
We can follow the same process as in the previous case:
C(12,4) = 12! / (4! * (12 - 4)!)
C(18,3) = 18! / (3! * (18 - 3)!)
c.) C(9,3), 6!
C(9,3) = 9! / (3! * (9 - 3)!)
6! = 6 * 5 * 4 * 3 * 2 * 1
To compare these two, we can evaluate both expressions.
d.) 3^5, 5!
3^5 represents 3 raised to the power of 5, which is calculated as 3 * 3 * 3 * 3 * 3.
5! is the factorial of 5, calculated as 5 * 4 * 3 * 2 * 1.
Now, we can compare the values obtained in each case to determine which number is larger.