SOLUTION: A group of Mathematics faculty at the local college consists of 10 women and 8 men. Four people are to be selected to go to a conference. How many different ways can a group of

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Question 1181276: A group of Mathematics faculty at the local college consists of 10 women and 8 men. Four people are to be selected to go to a conference.
How many different ways can a group of four people be selected from this group of 18?
In how many ways can four women be chosen from the group of 10 women ?
What is the probability that all women will be chosen to attend the conference? (enter reduce fraction or decimal)

Answer by ikleyn(52778) About Me  (Show Source):
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A group of Mathematics faculty at the local college consists of 10 women and 8 men.
Four people are to be selected to go to a conference.
(a) How many different ways can a group of four people be selected from this group of 18?
(b) In how many ways can four women be chosen from the group of 10 women ?
(c) What is the probability that all women will be chosen to attend the conference? (enter reduce fraction or decimal)
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(a)  In  C%5B18%5D%5E4 = %2818%2A17%2A16%2A15%29%2F%281%2A2%2A3%2A4%29 = 3060 ways.     ANSWER


(b)  In  C%5B10%5D%5E4 = %2810%2A9%2A8%2A7%29%2F%281%2A2%2A3%2A4%29 = 210 ways.         ANSWER


(c)  P = 210%2F3060 = 7%2F102 = 0.06863   (rounded).            ANSWER


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