Simplify 5C3
5C3 can be simplified as:
5C3 = 5! / ((5-3)! * 3!) [Using the formula for combinations: nCr = n! / (r! * (n-r)!)]
= 5! / (2! * 3!)
= (5 * 4 * 3 * 2 * 1) / (2 * 1 * 3 * 2 * 1)
= (5 * 4) / 2
= 10
Therefore, 5C3 simplified to 10.
To simplify 5C3, we need to calculate the value of the combination.
In general, the combination, denoted by nCr, represents the number of ways to choose r objects from a set of n objects without considering the order.
The formula for calculating a combination is given by:
nCr = n! / (r!(n-r)!)
In this case, we have n = 5 and r = 3.
So, substituting these values into the formula, we get:
5C3 = 5! / (3!(5-3)!)
To simplify further, let's calculate the factorial terms:
5! = 5 * 4 * 3 * 2 * 1 = 120
3! = 3 * 2 * 1 = 6
(5 - 3)! = 2! = 2 * 1 = 2
Now, let's substitute the factorial terms back into the combination formula:
5C3 = 120 / (6 * 2)
Simplifying the denominator:
5C3 = 120 / 12
Finally, performing the division:
5C3 = 10
Therefore, 5C3 simplifies to 10.