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# There are 8 job applicants sitting in a waiting room4 women and 4 men

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Re: There are 8 job applicants sitting in a waiting room4 women and 4 men [#permalink]
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There are 8 job applicants sitting in a waiting room—4 women and 4 men. If 2 of the applicants are selected at random, what is the probability that both will be women?

A. $$\frac{1}{4}$$

B. $$\frac{3}{7}$$

C. $$\frac{5}{2}$$

D. $$\frac{3}{14}$$

E. $$\frac{1}{10}$$

solve using probability method

$$\frac{4}{8}*\frac{3}{7} = \frac{12'}{56} = \frac{3}{14}$$

solve using combinatorics

Total number of ways $$P^8_2$$ = $$24$$

Number of ways to choose two women out of 4 $$P^4_2$$ = $$6$$

Number of ways to choose both women from 8 persons $$\frac{6}{24}$$
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Re: There are 8 job applicants sitting in a waiting room4 women and 4 men [#permalink]
There are 8 job applicants sitting in a waiting room—4 women and 4 men. If 2 of the applicants are selected at random, what is the probability that both will be women?

A. $$\frac{1}{4}$$

B. $$\frac{3}{7}$$

C. $$\frac{5}{2}$$

D. $$\frac{3}{14}$$

E. $$\frac{1}{10}$$

The probability that two women are selected is as follows:

4/8 x 3/7 = 1/2 x 3/7 = 3/14.