A baseball team has 12 players the coach needs to choose 3 to sit on the bench how many combinations of players can the coach choose? Show me the formula please

Question

need to find the formula for probability of a team with 12 players 3 have to sit on the bench how many combinations does the coach have show formula please

Answer 1

Look at the 12th row of pascals triangle and look at the 4th number from the left, tada!

Answer 2

The general formula for this kind of problem is the Combination formula nCr = n! ÷ [r!(n-r!)].

If this is a surprise, I think that you will profit from a careful re-reading of your textbook and other lecture material.

There are also NUMEROUS examples of such problems available in WyzAnt's Resources/Answers.

Answer 3

You need to choose 3 players.

How many choices do you have for the first player? 12. For the second? 11. For the third? 10. Sounds like 12*11*10...

But choosing players A, B, and C is the same as choosing players B, C, and A (for example). That is, choosing the same 3 players in a different order shouldn't count as another combination. 

So you need to divide by the number of ways to order the 3 players you choose. This way, you are counting the number of ways to arrange 3 players from a set of 12, divided by the number of ways to arrange 3 players, resulting in just the number of ways to choose 3 players from a set of 12, without counting different arrangements. There are 3!=3*2*1 ways of arranging 3 players. So your answer is 12*11*10/(3*2*1)

 

The general formula for this type of problem (NOTE: you must think about the type of problem before blindly applying a formula because there are different formulas for different situations, so it's always better to think through the problem each time) is n!/k!(n-k)! where n is the total number of the set you're choosing from, and k is the number of elements you choose. In this example, the formula looks like 12!/3!(12-3)!=12!/3!9!=12*10*11/(3*2*1)