+0

# HELP PLS!

+1
42
4
+274

Thomas, Carrie and Lenny each captain a different one of three hockey teams. Each captain will choose four players from a pool of 12 players, with each player chosen for only one team. How many different ways can the teams be formed?

May 22, 2023

#1
0

Thomas can choose from 12 players to form his team, Carrie can choose from the 8 remaining players, and Lenny can choose from the 5 remaining players. Therefore, there are 12×8×5=480​ ways to form the teams.

May 22, 2023
#2
+274
+1

Incorrect solution again... The answer is 34,650.

May 22, 2023
#3
+1

[12 nCr 4] * [8 nCr 4] * [4 nCr 4]==34,650 - different ways of picking the 3 teams.

Guest May 22, 2023
#4
+274
0

Correct! Here's the full and detailed solution. Let me know if you have any questions!

Thomas can choose any $$4$$ out of $$12$$ players, which is $$\binom{12}{4}$$ distinct possibilities for a team. Carrie can choose any $$4$$ out of the remaining $$8$$ players, which is $$\binom{8}{4}$$ distinct possibilities for a team. Lenny has only $$1$$ choice for his team, whichever $$4$$ have not yet been chosen. Combining all this yields

\begin{align*} \frac{12\times11\times10\times9}{4\times3\times2}\times\frac{8\times7\times6\times5}{4\times3\times2} &= 11\times 10 \times 9 \times 7 \times 5 \\ &= 99\times 35\times 10 \\ &= (3500-35)\times 10 \\ &= \boxed{34,650\text{ ways}}. \end{align*}

May 22, 2023