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) 3768650I had been asked this question in homework.I'm obligated to ask this question of Counting topic in portion Counting of Discrete Mathematics

A postman can put 12 letters into their respective envelopes such that

1.	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) 3768650I had been asked this question in homework.I'm obligated to ask this question of Counting topic in portion Counting of Discrete Mathematics
Answer» 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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