Solve all of these follwing Question: (E): A committee of 2 teachers is to be formed in a school such that there is one male and one female representative. In how many ways the committee can be formed if there are 15 male teachers and 12 female teachers. (F): Eight runners are hoping to take part in a race, but the track has only six lanes. In how many ways can six of the eight runners be assigned to lanes? (G): A typist has 5 letters and 5 addressed envelopes. In how many different ways can the letters be placed in each envelope WITHOUT getting EVERY letter in the RIGHT envelope? (I): How many 5-digit numbers can be created such that no digit is repeated? (Zero may appear at the start) (J): Your DS quiz has only 5 multiple choice questions, with each question consisting of 4 options. In how many ways these 5 MCQs can be answered if you could pick ONLY 1 OPTION OR LEAVE IT UNATTEMPTED
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.
Solve all of these follwing Question:
(E): A committee of 2 teachers is to be formed in a school such that there is one male and one female representative. In how many ways the committee can be formed if there are 15 male teachers and 12 female teachers.
(F): Eight runners are hoping to take part in a race, but the track has only six lanes. In how many ways can six of the eight runners be assigned to lanes?
(G): A typist has 5 letters and 5 addressed envelopes. In how many different ways can the letters be placed in each envelope WITHOUT getting EVERY letter in the RIGHT envelope?
(I): How many 5-digit numbers can be created such that no digit is repeated? (Zero may appear at the start)
(J): Your DS quiz has only 5 multiple choice questions, with each question consisting of 4 options. In how many ways these 5 MCQs can be answered if you could pick ONLY 1 OPTION OR LEAVE IT UNATTEMPTED
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