Question

Two numbers 'a' and 'b' are selected successively without replacement in that order from integers 1 to 10. The probability that a/b is an integer, is:-

(a) 17/45

(b) 1/5

(c) 17/90

(d) 8/45

Answer 1

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

So, total number of possible combination of a and b so that (a/2) is a fraction without replacement are: 

(1/2, 1/3, 1/4, .... 1/10)

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

= (9)(10)

= 90

Now the possible combination which makes (a/b) an integer without replacement are-

= (2/1, 3/1, 4/1, 5/1, 6/1, 7/1, 8/1, 9/1, 10/1, 4/2, 6/2, 6/3, 8/2, 8/4, 9/3, 10/2, 10/5)

= 17

Therefore the probability that (a/b) is an integer,

= [Possible combination which (a/b) an integer]/[Total Possible combination of (a/b)]

= 17/90.