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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.

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.

Grade:12

2 Answers

Priyansh Goel
21 Points
11 years ago

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!  = 10P2 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

h v
33 Points
10 years ago

thanks for the answer

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