How many combinations of players can a coach have if he needs to pick 2 out of a total of 4? what is a simpler way to find out

To find how many combinations of 2 players can be chosen from 4, you’re dealing with combinations (order doesn’t matter).

Simple Method (Combination Formula)

Use:

(nr)=n!r!(n−r)!\binom{n}{r}=\frac{n!}{r!(n-r)!}(rn​)=r!(n−r)!n!​

Here:

• n=4n=4n=4 (total players)
• r=2r=2r=2 (players to pick)

(42)=4!2!⋅2!=4⋅32⋅1=6\binom{4}{2}=\frac{4!}{2!\cdot 2!}=\frac{4\cdot 3}{2\cdot 1}=6(24​)=2!⋅2!4!​=2⋅14⋅3​=6

Even Simpler Way (No Formula Needed)

Just list them:

• Player 1 & Player 2
• Player 1 & Player 3
• Player 1 & Player 4
• Player 2 & Player 3
• Player 2 & Player 4
• Player 3 & Player 4

That’s 6 combinations.

Quick Trick to Remember

For small numbers:

• Think: “How many unique pairs can I make?”
• Or use:

n(n−1)2\frac{n(n-1)}{2}2n(n−1)​

So:

4⋅32=6\frac{4\cdot 3}{2}=624⋅3​=6

This shortcut works anytime you’re picking 2 items from a group. Final Answer: 6 combinations