Play match

A hockey match played for three periods ended with a score of 2:3. How many possibilities are there on how the given thirds could have been completed?

Correct answer:

n =  10

Step-by-step explanation:

$$\begin{gathered} C_3(5)=\left(\genfrac{}{}{0ex}{}{5}{3}\right)=\frac{5!}{3!(5-3)!}=\frac{5\cdot 4}{2\cdot 1}=10 \\ AABBB \\ ABABB \\ ABBAB \\ ABBBA \\ BAABB \\ BABAB \\ BABBA \\ BBAAB \\ BBABA \\ BBBAA \\ n=\left(\genfrac{}{}{0ex}{}{2+3}{3}\right)=10 \end{gathered}$$

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