0 math teachers, 6 physics teachers, and 4 chemistry teachers are on a committee. A subcommittee of 7 people is to be chosen. a) How many ways can this be done if there are no restrictions? b) In how many ways can one select a committee of 7 people having exactly 4 math teachers and at most 1 chemistry teacher? Help me fast
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.
10 math teachers, 6 physics teachers, and 4 chemistry teachers are on a committee. A subcommittee of 7 people is to be chosen.
a) How many ways can this be done if there are no restrictions?
b) In how many ways can one select a committee of 7 people having exactly 4 math teachers and at most 1 chemistry teacher?
Help me fast
Given,
10 maths teachers,6 physics teachers, and 4 chemistry teachers are on a committee. and
A subcommittee of 7 people is to be chosen.
Part a:
We know that,
We can choose,
from with a number of ways
Here,
There are 20 teachers,
We want to choose 7 from 20.
Therefore the number of ways we can choose is
Now,
Therefore we can choose 7 people from 20 teachers with 77520 ways.
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