Two numbers a and b are selected successively without replacement in that order from the 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 

Solution:

Total numbers of elementary events are: 10 ×9 = 90

(numbers are of non-replacing nature and order matters)

Let E be an event that a/b is an integer.

Favourable events = 2/1, 3/1, 4/1, 5/1, 6/1, 7/1, 8/1, 9/1, 10/1, 4/2, 6/2, 8/2, 10/2, 6/3, 9/3, 8/4, 10/5.

Number of favourable events = 17

Required probability = 17/90

Hence option c is the answer.

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