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.