If 6 boys and 3 girls are to be seated in a row for a photograph, then the probability that the end seats are occupied by the girls and no two girls are side by side is

Question

The distribution function $ F(X) $ of a discrete random variable $ X $ is given. Then $ P[X = 4] + P[X = 5] $:
\[ \begin{array}{|c|c|c|c|c|c|c|} \hline X & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline F(X = x) & 0.2 & 0.37 & 0.48 & 0.62 & 0.85 & 1 \\ \hline \end{array} \]

Answer 1

Step 1: Seats of girls
Two girls take seats 1 and 9. The third girl must avoid seats 2 and 8, so she may take seats 3 to 7: 5 choices.

Step 2: Names and boys
Assign the 3 girls to their 3 seats in $3!$ ways and the boys to the other 6 seats in $6!$ ways.

Step 3: Ratio
$P = \dfrac{5 \cdot 6 \cdot 720}{362880} = \dfrac{21600}{362880} = \dfrac{5}{84}$. Option (D).

Final Answer:
Option (D). \[ \boxed{\frac{5}{84}} \]

If 6 boys and 3 girls are to be seated in a row for a photograph, then the probability that the end seats are occupied by the girls and no two girls are side by side is

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The Correct Option is D

Solution and Explanation

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