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

विकल्प

• \[\frac{17}{45}\]

• \[\frac{1}{5}\]

• \[\frac{17}{90}\]

• \[\frac{8}{45}\]

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`