A girl has 12 friends. 5 are male and 7 are female. She can only invite 8 people to her house because her dining table only seats 8. What is the probability that there will be 4 males and 4 females...

A girl has 12 friends. 5 are male and 7 are female. She can only invite 8 people to her house because her dining table only seats 8. What is the probability that there will be 4 males and 4 females at the party.

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The girl has 12 friends of which 5 are male and 7 are female. She invites 8 people to her house as her dining table can seat only that many. The probability that there will be four males and four females at the party has to be determined.

The total number of ways of choosing 8 people from a set of 12 is 12C8 = 495. The number of ways of choosing 4 males and 4 females is 5C4 = 5 and 7C4 = 35 respectively. Multiplying the two gives 175. The probability of an event happening is the number of ways favorable to the event divided by the total number of ways that events can take place in. Here, the total number of ways that the friends can be chosen is 495 and the number of ways of choosing 4 males and 4 females is 175. This gives the probability of the event as 175/495 = 35/99.

There is a 35/99 probability that there will be 4 males and 4 females at the party.

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