Probability of Love...

When 55 friends, Satvik, Agnishom, Mursalin, Sandeep and Aditya enter engineering college, they see 1010 lovely girls, each one equally attractive...

Each of the 55 boys falls in love with one of the 1010 girls at random, independently of each other.

The probability that the 55 boys all fall in love with different girls when each boy randomly chooses one of the 1010 girls as the girl they love, can be expressed as ab\dfrac{a}{b} where aa and bb are co-prime positive integers.

Find the value of a+ba+b.

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