Question

Asked Nov 4, 2019

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^{ 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?}

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 14^{28} = 1.23477 × 10^{32} ways.

Thus, the number of ways in which the 28 cards can be put into the 14 envelopes, if the cards are distinct, is **14 ^{28}** or

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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