How many combinations are there of six distinct objects taken three at a time?
http://www.mathwords.com/c/combination_formula.htm
To find the number of combinations of six distinct objects taken three at a time, we can use the combination formula.
The combination formula is given as:
C(n, r) = n! / (r! * (n - r)!)
Where:
n is the total number of objects,
r is the number of objects taken from the total,
! denotes factorial, which is the product of an integer and all the positive integers below it.
In this case, we have n = 6 objects and r = 3 objects.
Plugging the values into the formula:
C(6, 3) = 6! / (3! * (6 - 3)!)
Simplifying:
C(6, 3) = (6 * 5 * 4 * 3!) / (3! * 3!)
The three factorials in the numerator and denominator cancel out:
C(6, 3) = (6 * 5 * 4) / (3 * 2 * 1)
Evaluating the expression:
C(6, 3) = 20
Therefore, there are 20 combinations of six distinct objects taken three at a time.