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A postman can put 12 letters into their respective envelopes such that exactly 5 will go into the right envelope. Find the number of ways of doing this work.

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A postman can put 12 letters into their respective envelopes such that exactly 5 will go into the right envelope. Find the number of ways of doing this work.

(a) 2984300

(b) 1610496

(c) 5322167

(d) 3768650

I had been asked this question in homework.

I'm obligated to ask this question of Counting topic in portion Counting of Discrete Mathematics

1 Answer

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Correct choice is (b) 1610496

Explanation: The number of ways in which the 5 correct envelopes can be selected = ^12C5 = 864

Derangement of the remaining 7 envelopes & letters = 1864 (derangement value for 7 is 1864)

Total No of ways of arrangement = 1864 * 864 = 1610496.

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