A basketball coach was criticized in the newspaper for not trying out every combination of players. If the team roster has 12 players, how many 5-player combinations are possible? Please help I'm having a hard time with this problem!!! :(
12C5 ... 12! / [(12 - 5)! * 5!]
the built in windows calculator has a factorial (!) key
To find the number of 5-player combinations from a roster of 12 players, you can use the concept of combinations. The formula for combinations is given by:
C(n, r) = n! / (r! * (n - r)!)
Where "n" is the total number of players, and "r" is the number of players in each combination.
In this case, you want to find the number of 5-player combinations from a roster of 12 players. Plugging in the values into the formula, we have:
C(12, 5) = 12! / (5! * (12 - 5)!)
Calculating the factorial values:
12! = 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 479,001,600
5! = 5 * 4 * 3 * 2 * 1 = 120
(12 - 5)! = 7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040
Now substituting these values back into the formula:
C(12, 5) = 479,001,600 / (120 * 5,040)
Performing the calculations:
C(12, 5) = 479,001,600 / 604,800 = 792
Therefore, there are 792 different 5-player combinations possible from a roster of 12 players.
To find the number of combinations, you can use the formula for combinations, which is given by:
C(n, r) = n! / (r! * (n - r)!)
Where n is the total number of objects and r is the number of objects chosen at a time.
In this case, you want to find the number of 5-player combinations out of a roster of 12 players.
Using the formula, the number of combinations can be calculated as follows:
C(12, 5) = 12! / (5! * (12 - 5)!)
Calculating this expression step by step:
12! / (5! * 7!)
= (12 * 11 * 10 * 9 * 8) / (5 * 4 * 3 * 2 * 1 * 7)
= (95,040) / (120 * 7)
= (95,040) / (840)
= 114
So, there are 114 possible 5-player combinations that can be chosen from a roster of 12 players.