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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
Options
\[\frac{17}{45}\]
\[\frac{1}{5}\]
\[\frac{17}{90}\]
\[\frac{8}{45}\]
Solution
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`
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