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A group of five persons is formed from five boys and four girls. Find the probability that there are at least two girls in the group?

Correct Answer: 110/129

Explanation:

Total number of possible ways = 


9 C 5   =   9   x   8   x   7   x   6   x   5 5   x   4   x   3   x   2   x   1   =   126


Number of favorable cases = 


4 C 2   x   5 C 3   +   4 C 3   x   5 C 2   +   4 C 4   x   5 C 1 4   x   3 2   x   1   x   5   x   4   x   3 3   x   2   x   1   +   4   x   3   x   2 3   x   2   x   1   x   5   x   4   2   x   1   +   1   x   5 =   6   x   10   +   4   x   10   +   5 =   60   +   40   +   5 =   105


 


Therefore, required probability = 105/126 = 5/6


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