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There are 6 letters and 6 directed envelopes. Find the number of ways in which the letters can be put into the envelopes so that all are not put in directed envelopes?

There are 6 letters and 6 directed envelopes. Find the number of ways in which the letters can be put into the envelopes so that all are not put in directed envelopes? Correct Answer 719

Explanation:

Here, the first letter can be put in any one of the 6 envelopes in 6 ways.

Second letter can be put in any one of the 5 remaining envelopes in 5 ways.

Continuing in this way, we get the total number of ways in which 6 letters can be put into 6 envelopes = 6 × 5 × 4 × 3 × 2 × 1 = 720

Since out of the 720 ways, there is only one way for putting each letter in the correct envelope. Hence, the number of ways of putting letters all are not in directed envelopes = 720 – 1 = 719 ways.

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