If a class of children is separated into groups of 5 children, 2 children will be left over. If the class is separated into groups of 6 children, 3 children will be left over. What is the smallest number of children the class could have? Just enter the number. 10 There is an even number between 200 and 300
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.
Let the number of children in the class is N.
1. It is given that when the children are seperated into groups of 5 children, 2 children are left over. It means when this N is divided by 5 we get remainder as 2.
2. And it is also given that when the children are seperated into groups of 6 children, 3 children are left over. It means when this N is divided by 6 we get remainder as 3.
Now N dividing by 5 it leaves a remainder of 2. Then if we add 3 to it, it would be perfectly divisible by 5. That is N+3 is a multiple of 5.
Similarly when N dividing by 6 it leaves a remainder of 3. Then if we add 3 to it, it would be perfectly divisible by 6. That is N+3 is also a multiple of 6.
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