Question

Two numbers 'a' and 'b' are selected successively without replacement in that order from the integers 1 to 10. The probability that $\frac{a}{b}$ is an integer, is

(a) $\frac{17}{45}$

(b) $\frac{1}{5}$

(c) $\frac{17}{90}$

(d) $\frac{8}{45}$

Answer 1

We have a set of natural numbers from 1 to 10 where andare two variables which can take values from 1 to 10.

So, total number of possible combination of and so that is a fraction without replacement are:

Similarly we have 9 such sets of 10 elements each. So total number of possible combination,

Now the possible combination which makes an integer without replacement are-

Therefore the probability thatis an integer,

The correct answer is option