A row of seats in a movie hall contains 10 seats. 3 Girls and 7 boys need to occupy those seats. What is the probability that no two girls will sit together?
Answers:
A) 7/15
B) 2/15
C) 4/15
D) 6/15
E) 9/15
Total # of ways for the 7 boys to stand = 7!   After these boys have stood in their positions, there are 8 positions for the 3 girls to occupy.   # of ways for the girls to choose 3 positions = 8C3   # of ways of arranging themselves = 3!   Hence, total # of ways for the girls = 8C3 times 3!   Overall, # of ways when no two girls are together = 7! times 8C3 times 3!   n(S) = n(Sample space for these 10 students) = 10!   Hence, probability for no two girls to sit together = 7! * 8C3 * 3! / 10!   = 8C3 * 3! / (10 * 9 * 8)   = (8 * 7 * 6 ) / (10 * 9 * 8)   = (7*6) / (10*9)   =7/15   7/15NSWER:7/15
<result>A</result>
A row of seats in a movie hall contains 10 seats. 3 Girls and 7 boys need to occupy those seats. What is the probability that no two girls will sit together?