What is the probability of randomly arranging the word CHALLENGING so that the first two letters are GG? Please explain.

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Question:

What is the probability of randomly arranging the word CHALLENGING so that the first two letters are GG? Please explain. 

Answer:

Explanation of above question is provided below:
First two letters are GG which is fixed. So number of ways for first two letters = 2P2.
Now 9 letters are remaining which can be arranged in 9P9 ways. 
Total number of ways when first two letters are GG is multiplication of above two cases. 
To find probability we need total number of ways without any condition. 
Total number of ways = 11!
Then probability is calculated as shown below. 
Final answer of probability = 0.0182
If you have any queries regarding above solution then please comment below. Thank you! 

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