12) Determine the number of ways each situation can occur. a) 3 out of 9 toppings for an ice cream sundae. b) Selecting 2 out of 25 students for a class project. c) Selecting the first place and second place horse in a 12-horse race.
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.
12) Determine the number of ways each situation can occur.
a) 3 out of 9 toppings for an ice cream sundae.
b) Selecting 2 out of 25 students for a class project.
c) Selecting the first place and second place horse in a 12-horse race.
Permutation :
we use permutation for the lists. For permutation the order matters
For combination the order does not matters
(a) 3 out of 9 toppings for an ice cream sundae.
We need to select 3 out of 9. Here the order does not matters . So we use combination
84 ways
b) Selecting 2 out of 25 students for a class project.
HEre also the order of students does not matters. So we use combination
300 ways
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