For 3 person relay, a coach can choose from 4 of his top runners. How many different 3- person teams can he choose?
4 choose 3
= C(4,3)
= 4
e.g.
A B C D
you can choose any 3 out of those 4
which means one letter is left out for each choice,
since there are 4 letters,
the number of ways to leave one letter out is 4
tha is,
A B C
A B D
B C D
A C D
24
To find the number of different 3-person teams the coach can choose from 4 top runners, we can use the formula for combinations.
The formula for combinations is given by:
C(n, r) = n! / (r!(n-r)!)
Where:
- C(n, r) represents the number of combinations of n items taken r at a time.
- n! represents the factorial of n, which is the product of all positive integers from 1 to n.
- r! represents the factorial of r.
- (n - r)! represents the factorial of the difference between n and r.
In this case, the coach has 4 runners to choose from, and he wants to form teams of 3. Therefore, n = 4 and r = 3.
Using the formula, we can calculate the number of different 3-person teams the coach can choose:
C(4, 3) = 4! / (3!(4-3)!)
= 4! / (3! x 1!)
= (4 x 3 x 2 x 1) / [(3 x 2 x 1) x 1]
= 24 / (6 x 1)
= 4
Therefore, the coach can choose from 4 different 3-person teams.