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?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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?
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
