suppose you want to select three people to form a committee from a group of 12, how many groups of 3 are possible? show steps

Answer 1

We want to choose 3 items from a group of 12. The general formula for the number of combinations of r items chosen from a group of n items is:

nCr = n! / (r!(n-r)!)

In this formula, the ! is not because we are excited, it is the mathematical operator "factorial."

In our question, we have n = 12 and r = 3, so we have:

₁₂C₃ = 12! / ((3!)(12-3)!)

= 12! / 3! * 9!

= (1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12) / ((1 x 2 x 3)(1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9))

We can cancel out the 1 through 9 and get:

(10 x 11 x 12) / (1 x 2 x 3)

= 1320 / 6

= 220

So there are 220 possible combinations of 3 people chosen from a group of 12.