Nine graduate students have applied for two available teaching assistantships. In how many ways can these assistantships be awarded among the applicants if (a) No preference is given to any one student? ways (b) One particular student must be awarded an assistantship? ways (c) The group of applicants includes five men and four women and it is stipulated that at least one woman must be awarded an assistantship?
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.
Nine graduate students have applied for two available teaching assistantships. In how many ways can these assistantships be awarded among the applicants if
ways
(b) One particular student must be awarded an assistantship?
ways
(c) The group of applicants includes five men and four women and it is stipulated that at least one woman must be awarded an assistantship?
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