Question

10) the batting order for 9 players on a 12 person team a.220b.79,822,600c.78,843,585d.78,837,12811) Kaitlin has hw in 7 subjects. she is decidin what order to complete them in.a.5040b.5495c.1d.442012)A team of 13 feild hockey players needs to choose 2 players to refill the water cooler.a.87b.75c.44d.78

Answer 1

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,

`\begin{gathered} ^(12)C_9=(12!)/(9!*(12-9)!) \\ ^(12)C_9=(12!)/(9!*3!) \\ ^(12)C_9=(12*11*10*9!)/(9!*3!) \\ ^(12)C_9=(12*11*10)/(6) \\ ^(12)C_9=220 \end{gathered}`

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,

`\begin{gathered} ^(13)C_2=(13!)/(2!*(13-2)!) \\ ^(13)C_2=(13!)/(2!*11!) \\ ^(13)C_2=(13*12*11!)/(11!*2!) \\ ^(13)C_2=13*6 \\ ^(13)C_2=78 \end{gathered}`

Hence, the number of ways the player has to be choosen are 78.

Therefore, option d is correct.