You are at a Carnival .One of the Carnival games ask you to pick a door and then pick a curtain behind the door. There are 3 doors and 4 curtains behind each door.how many choices are possible for the player ?????

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jurrasicanada jurrasicanada · Answer 1 · 2017-09-15T23:35:53+02:00

Number of possibilities = number of doors x number of curtains

3x4=12

Therefore, there are 12 possibilities.

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PratikshaS PratikshaS · Answer 2 · 2022-07-02T05:18:59+02:00

There are 12 possible choices for the player.

"It is a way of selecting items from a collection "

"[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]"

n! = n × (n - 1) × . . . × 2 × 1

For given question,

There are 3 doors and 4 curtains behind each door.

The number of possible ways of selecting a door from the 3 doors.

Using combination formula,

[tex]^3C_1=\frac{3!}{1!(3-1)!}\\\\ ^3C_1=\frac{3\times 2!}{2!}\\\\ ^3C_1=3[/tex]

The number of possible ways of selecting a curtain from the 4 curtains.

Using combination formula,

[tex]^4C_1=\frac{4!}{1!(4-1)!}\\\\ ^4C_1=\frac{4\times 3!}{3!}\\\\ ^3C_1=4[/tex]

So, the number of choices for the player to pick a door and then pick a curtain behind the door :

[tex]^3C_1\times ^4C_1\\\\=3\times 4\\\\=12[/tex]

Therefore, there are 12 possible choices for the player.

Learn more about combination here:

https://brainly.com/question/13387529

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