Suppose there are 5 men and 8 women qualified to be members of a new committee of 6 people, including a president, a vice-president, and a secretary. (a) How many different ways do you have to pick a president, vice-president and secretary if you need at least 1 men and 1 women? Does the order matter? Why? (b) How many different committees can you form with at least 3 women? Does the order matter? Why?
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.
Suppose there are 5 men and 8 women qualified to be members of a new committee of 6 people, including
a president, a vice-president, and a secretary.
(a) How many different ways do you have to pick a president, vice-president and secretary if you need at
least 1 men and 1 women? Does the order matter? Why?
(b) How many different committees can you form with at least 3 women? Does the order matter? Why?
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
