The number of distinct rational numbers $$x$$ such that $$0 < x < 1$$ and $$x = \frac{p}{q},$$ where $$p,q \in \left\{ {1,2,3,4,5,6} \right\},$$ is
A.
15
B.
13
C.
12
D.
11
Answer :
11
Solution :
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 $$= 15 - 4 = 11.$$
Releted MCQ Question on Algebra >> Permutation and Combination
Releted Question 1
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