Final answer:
The probability that the five girls will sit together in a row when seated at random with 5 boys is calculated by treating the girls as one unit and considering the permutations. The probability is found to be d. 1/10.
Step-by-step explanation:
The question asks for the probability that the five girls sit together when 5 boys and 5 girls are seated in a row at random. To solve this, we can treat the 5 girls as one unit since they must sit together, giving us 6 units to arrange (5 girls as 1 unit and 5 boys). There are 6! ways to arrange these units.
However, the girls can be arranged among themselves in 5! ways. So the total favorable arrangements are 6! * 5!. The total possible arrangements without any restriction are 10! because there are 10 individuals. Thus, the probability is the number of favorable outcomes divided by the number of total possible outcomes: P = (6! * 5!) / 10!.
Now calculating the probability:
P = (6! * 5!) / 10! = (720 * 120) / 3628800 = 1/10
Therefore, the correct answer is d. 1/10.