How many ways are there to select a committee of 17 politicians chosen from a room full of indistinguishable Democrats, indistin
guishable Republicans, and indistinguishable Independents if every party must have at least two members on the committee? If, in addition, no group may have a majority of the committee members?
In order to have majority, the number of members is one party must be greater than the number of members in other party.
This means that one of the party must have at least 9 members.
a) Every party must have at least two members on the committee
b) no group may have a majority of the committee members
Since , both the parties cannot have 9 members thus in order to compute the committee number in a way that no group may have a majority of the committee members
A mosquito net is a type of meshed curtain that is circumferentially draped over a bed or a sleeping area, to offer the sleeper barrier protection against bites and stings from mosquitos, flies, and other pest insects, and thus against the diseases they may carry
The Earth's atmosphere protects us from the multitude of small debris, the size of grains of sand or pebbles, thousands of which pelt our planet every day. So the probability of a major collision is quite small