# There are three women and four men in a group of seven people. If three people are selected from the total of seven, find the following: i)What are th

There are three women and four men in a group of seven people. If three people are selected from the total of seven, find the following: i)What are the total possible outcomes for this selection? ii)How many ways can two women and one man be selected? iii)What is the probability of selecting two women and one man?

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SchepperJ

1) you choose 3, possible ways: choose 3 women, 1 solution, choose 3 men; 3 solution, choose 2w 1m: $$\displaystyle{3}\cdot{4}={12}$$, choose 2m 1w: $$\displaystyle{6}\cdot{3}={18}$$. Total $$1+4+12+18=35$$
2) from 3 women you choose 2, that is 3 ways, and from 4 men you choose 1, that is four, multiplying $$3 \cdot 4=12$$ ways.
3) there is 12 ways from 35, that means probability is $$\displaystyle\frac{{12}}{{35}}$$.