a. If there are 8 different colors of foot balls are available in a sports shop, in how many wavs can choose two-foot balls at a time. b. A college supports hall has seven doors. In how many ways can a student entre the supports hall through one door and come out through a different door? c. How many three-digit numbers less than 800 can be formed by using the digits 3, 4, 5, 6, 7 and 8? When repetition of digits is not allowed.
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.
b)
There are 7 door in college support hall. A student can enter only of door but out through a different door:
There are 7 door to get enter and 6 door to get out (cannot out from entering door).
So, there are 7*6 =42 ways a student can enter the support hall through one hall and comes out through a different door.
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