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  • In a lottery game, there are 12 numbered balls (1 to 9) in a machine. If you randomly draw 6 balls without replacement, how many different combinations of 4 balls can you obtain?<div class='qna

In a lottery game, there are 12 numbered balls (1 to 9) in a machine. If you randomly draw 6 balls without replacement, how many different combinations of 4 balls can you obtain?

Option: 1

30420


Option: 2

22480


Option: 3

53480


Option: 4

42320


Answers (1)

best_answer

The number of permutations of 4 balls chosen from 12 balls is given by,

{ }^{12} P_6

Using the Permutations formula,

{ }^n P_r=\frac{n !}{(n-r) !}

Solving the above term to get,

\begin{aligned} & { }^{12} P_4=\frac{12 !}{(12-4) !} \\ & { }^{12} P_4=\frac{12 !}{8 !} \\ & { }^{12} P_4=40320 \end{aligned}

Therefore, in 40320 ways, 4 balls can be chosen in a lottery game.

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