Asked Nov 4, 2019

 You have 28 cards and 14 envelopes (labeled 1,2, ..,14).
In how many ways can you put the 28 cards into the envelopes if

(a) The cards are distinct?

Answer = 

(b) The cards are identical?

Answer = 

(b) The cards are identical and no envelope can be left empty?


Expert Answer

Step 1

Part a:

The envelopes are numbered 1 to 14.

Each of these 14 envelopes can hold any of the 28 distinct cards.

This is possible in 1428 = 1.23477 × 1032 ways.

Thus, the number of ways in which the 28 cards can be put into the 14 envelopes, if the cards are distinct, is 1428 or 1.23477 × 1032.

Step 2

Part b:

It is given that the 28 cards are identical.

This suggests that the 28 identical cards can be allocated to the 14 numbered envelopes in (28 + 14 – 1)C(14 – 1) = 41C13 or 17,620,086,360 ways.

Thus, the number of w...

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