dear sir/madam, i am having doubt in the following question for some time now and iit is on 11th ,so please help...!!

Q) "How many different rational numbers are there using 10 different prime numbers?"

The answer given is 91 and the explanation is:- 10P2 + 1=91. I cannot understand how.Please help.

A rational no. is of form a/b where a and b are coprime. Now, understand these steps:

1. Select 2 no. from 10 prime no. to represent in form a/b in ¹⁰C₂ ways.

2.  Permute the two selected no. in 2! ways.

3.  So, total ways of permuting these two numbers is ¹⁰C₂* 2!  = ¹⁰P_{2 ways.}

3. now we have not included the cases when the two numbers selected would be same. They all will give one result i.e. 1. So adding 1 to the got result we get our answer as 91

thanks for the answer