Question

wo council members have the same major and are not permitted to serve together on a committee. how many ways can a committee of five be selected from the membership of the council?

1. Tryphena
The total number of methods to select the five-person committee and guarantee that there aren’t any members with the same major is= 4004ways.

What is Probability?

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with ‘n’ outcomes can be represented by the symbol x.
The probability of an event can be calculated using the following formula.
Probability(Event) = Positive Results/Total Results = x/n
In order to better grasp probability, let’s look at a straightforward application.
Let’s say we need to forecast if it will rain or not. Either “Yes” or “No” is the appropriate response to this query.
There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.
According to our question-
From the two students with same major we also use the combination Formula in knowing the number of ways any of the two students can be chosen. To choose one from these two students, we use the combination Formula 2C1.
the two students with same major aren’t on the committee becomes:
14C5 * 2C1
2002 * 2
4004ways.