SATHEE: Permutations And Combinations Question 339

Permutations And Combinations Question 339

Question: The number of distinct rational numbers x such that $ 0<x<1 $ and $ x=\frac{p}{q}, $ where $ p,q\in {1,2,3,4,5,6}, $ is

Options:

A) 15

B) 13

C) 12

D) 11

Show Answer

Answer:

Correct Answer: D

Solution:

[d] As $ 0<x<1, $ we have $ p<q $ The number of rational numbers $ =5+4+3+2+1=15. $ When p, q have a common factor, we get some rational numbers which are not different from those already counted. There are 4 such numbers: $ \frac{2}{4},\frac{2}{6},\frac{3}{6},\frac{4}{6} $ Therefore, required number of rational numbers $ =15-4=11. $

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Permutations And Combinations Question 339

Question: The number of distinct rational numbers x such that $ 0<x<1 $ and $ x=\frac{p}{q}, $ where $ p,q\in {1,2,3,4,5,6}, $ is

Options:

Answer:

Solution:

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