Evaluate 5^C3
????
Did you mean C(5,3) or 5C53 ?
If so, then
C(5,3) = 5!/(3!2!) = 120/(6(2)) = 120/12 = 10
in general
C(n,r) , read "n choose r"
= n!/( ( n-r)!r! )
It should be:
like the second one you put but 5 ^C3(not the extra 5 after the C)....its very confusing to me :(
To evaluate 5^C3, we first need to understand what the notation "5^C3" represents.
In mathematics, the symbol "^" denotes exponentiation, meaning raising a number to a power. The expression "5^C3" suggests that we are raising 5 to the power of the combination of 3.
A combination is a way to select items from a larger set without regard to the order in which the items are chosen. The formula for combinations, denoted as "C(n, r)" or "nCr," is given by:
C(n, r) = n! / (r! * (n - r)!)
In this formula, "n" represents the total number of items or elements, and "r" represents the number of items to be chosen.
Now, let's calculate 5^C3 step by step:
STEP 1: Calculate the combination.
We have n = 5 and r = 3.
C(5, 3) = 5! / (3! * (5 - 3)!)
= 5! / (3! * 2!)
= (5 * 4 * 3 * 2 * 1) / ((3 * 2 * 1) * (2 * 1))
= 10
Therefore, C(5, 3) equals 10.
STEP 2: Raise 5 to the power of the calculated combination.
5^C3 = 5^10
Now, evaluating 5^10 using a calculator or by manual computation:
5^10 = 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5
= 9,765,625
Therefore, the value of 5^C3 is 9,765,625.