The sum of the digits of a two-digit number is 11. If the digits are interchanged, the new number is 27 larger than the original number. Find the number.
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.
![3. The sum of the digits of a two-digit number is 11. If the digits are interchanged, the new
number is 27 larger than the original number. Find the number.
4. A man can row 4 km per hour in still water finds that he can row upstream in 7- hours a
distance which require 2- hours to row downstream. Find the rate of the current.
5. The perimeter of a rectangle is 178 meters. If 4 meters were added to its width, the sum is
half its length. What are its dimensions?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F55f2977a-7cb5-4f18-9ebc-43fa8e992b0a%2F1763b4a1-f045-475f-b7f0-83d3bed77650%2F8me91h_processed.jpeg&w=3840&q=75)
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