Question

Class 10th // Maths.
Two numbers $a$ and $b$ are selected without replacement in that order form the integers 1 to 10. Find the probability for $\dfrac{a}{b} \in Z$ .

Answer 1

So this question is a combination of (permutation & combination) + Probability.

Before finding probability we must know total possible outcomes.

Total possible ways of selecting 2 numbers from a set of '1' to '10' are:-

2(10!/2!x8!)=90

Now we need to count the events when given condition of a/b=z satisfy for this we need to make cases.

case 1

When b is 1 'a' can be (2,3,4,5,6,7,8,9,10) =

9 events

Case 2

When b is 2 'a' can be (4,6,8,10)=4 events

case 3

When b is 3 'a' can be (6,9)= 2 events

Case 4

When b is 4 'a' can be (8 only) = 1 event

Case 5

When b is 5 'a' can be ( 10 only) = 1 event

Total events satisfying condition=

17

Total outcomes=90

Probability=17/90