A team of 3 students is being chosen from a committee of 15. Find the number of different team can be formed. The committee consists of 10 boys in which two of them are twin and 5 girls. (a) If the twin must be in the team, how many ways can this be done. (b) If the team must contain at least one boy and at least one girl, how many ways can this be done. (c) If only one of the twin must be in the team, how many ways can this be done?
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 team of 3 students is being chosen from a committee of 15. Find the number of different
team can be formed. The committee consists of 10 boys in which two of them are twin and 5
girls.
(a) If the twin must be in the team, how many ways can this be done.
(b) If the team must contain at least one boy and at least one girl, how many ways can this
be done.
(c) If only one of the twin must be in the team, how many ways can this be done?
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