Given,
10)The total number of players are 12.
The number of player has to be chosen for batting is 9.
The number of ways of choosing 9 player from 12 player is,
[tex]\begin{gathered} ^{12}C_9=\frac{12!}{9!\times(12-9)!} \\ ^{12}C_9=\frac{12!}{9!\times3!} \\ ^{12}C_9=\frac{12\times11\times10\times9!}{9!\times3!} \\ ^{12}C_9=\frac{12\times11\times10}{6} \\ ^{12}C_9=220 \end{gathered}[/tex]Hence, the number of ways the player has to be choosen are 220.
Therefore, option a is correct.
11) The number of subjects Kaitlin have 7.
The number of arranging the 7 subjects is,
7! = 5040
There are 5040 possible arrangment of the 7 subjects.
Therfore, option a is correct.
12)The total number of players are 13.
The number of player has to be chosen for water refill is 2.
The number of ways of choosing 2 player from 13 player is,
[tex]\begin{gathered} ^{13}C_2=\frac{13!}{2!\times(13-2)!} \\ ^{13}C_2=\frac{13!}{2!\times11!} \\ ^{13}C_2=\frac{13\times12\times11!}{11!\times2!} \\ ^{13}C_2=13\times6 \\ ^{13}C_2=78 \end{gathered}[/tex]Hence, the number of ways the player has to be choosen are 78.
Therefore, option d is correct.
