Vincen wrote:Five people, Ada, Ben, Cathy, Dan, and Eliza, are lining up for a photo. What is the probability that none of the three girls will stand next to one another?
(A) 0.1
(B) 0.2
(C) 0.3
(D) 0.4
(E) 0.5
For the 3 girls to be separated, they must occupy the first, third and fifth positions, as follows:
G_G_G.
P(girl occupies the first position) = 3/5. (Of the 5 children, 3 are girls.)
P(girl occupies the third position) = 2/4. (Of the 4 remaining children, 2 are girls, since 1 of the 3 girls occupies the first position.)
P(girl occupies the fifth position) = 1/3. (Of the 3 remaining children, only 1 is a girl, since 2 of the 3 girls occupy the first and third positions.)
To combine these probabilities, we multiply:
3/5 * 2/4 * 1/3 = 1/10.
The correct answer is
A.
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