12 balls numbered 1 through 12 are placed in a bin. In how many ways can 3 balls be drawn, in order, from the bin, if the first ball is replaced after it is drawn but the second ball remains outside the bin?

Question

Cale

Mathematics

23 January, 20:19

12 balls numbered 1 through 12 are placed in a bin. In how many ways can 3 balls be drawn, in order, from the bin, if the first ball is replaced after it is drawn but the second ball remains outside the bin?

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Answers (1)

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Lyric Todd · Answer 1

1584

Step-by-step explanation:

There are 12 ways of drawing the first ball (it can be any of them). This ball is replaced by a different one, so we still have 12 balls in the bin.

The second ball can be chosen in 12 ways. This ball is removed from the bin, so now we have 11 balls in the bin.

Finally, for the third ball, we can choose any of the remaining 11 balls. Thus, there are 12*12*11=1584 ways of drawing the 3 balls.