1. Find the number of distinguishable permutations of the digits of the number 3,283,882,432,599. 2. In how many ways can 12 people occupy the circular table in a mini theatre? 3. How many ways can 5 bicycles be parked if there are 9 available parking spaces? 4. How many distinguishable permutations are possible with all the letters of the word MISSISSIPPI?
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.
1. Find the number of distinguishable permutations of the digits of the number 3,283,882,432,599.
2. In how many ways can 12 people occupy the circular table in a mini theatre?
3. How many ways can 5 bicycles be parked if there are 9 available parking spaces?
4. How many distinguishable permutations are possible with all the letters of the word MISSISSIPPI?
5. P (11,4)
6. P (20,2)
7. In how many ways can 10 people be seated around a circular table?
8. Find the number of permutations of the letters of the word TRIGONOMETRY.
9. A tailor owner has 10 new pants that he wants to display in the window. If the display window has 4 mannequins, in how many ways can he dress them up?
10. If there are 15 people and only 2 chairs are available, in how many ways can they be seated?
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