There are \(C_1^{600}\) or 600 ways of choosing a certain safe deposit box.
Similarly, there are \(C_1^{700}\) or 700 ways of choosing a key to open the box.

To open the box, the thief must choose the corresponding 300 boxes for which he has the keys.

Therefore, the probability that the thief will be able to open the box is \(\frac{1*300}{600*700} = \frac{1}{1400}\)

PS: please post the question under the right subforum: ps is it is a ps, numeric entry if it is a NE.

Moreover, this should be a problem solving

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