A laboratory cage contains eight white mice and six brown mice. Find the number of ways of choosing five mice from the cage if They can be of either colour? At least one of each colour must be chosen? It must have at most two white mice?
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.
A laboratory cage contains eight white mice and six brown mice. Find the number of ways of choosing five mice from the cage if
- They can be of either colour?
- At least one of each colour must be chosen?
- It must have at most two white mice?
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