two number a and b are selected successful y without replacement in that order from the integer 1 to 10 the probably that a/bis an integer is
Answers
The two numbers a and b are taken successively without replacement in that order. So the total no. of outcomes is ¹⁰C₁ × ⁹C₁ = 10 × 9 = 90.
Now we need to find the no. of outcomes for which a/b is an integer.
Since the two numbers are taken without replacement, we see that a ≠ b.
If b = 1, then a can be any among the remaining 9 numbers 2, 3, 4,..., 10. So no. of outcomes for which a/b is an integer and b = 1 is 9 × 1 = 9.
If b = 2, then a can be any among the 4 numbers 4, 6, 8, 10. So no. of outcomes for which a/b is an integer and b = 2 is 4 × 1 = 4.
If b = 3, then a can be any among the 2 numbers 6, 9. So no. of outcomes for which a/b is an integer and b = 3 is 2 × 1 = 2.
If b = 4, then a = 8 only. So no. of outcomes for which a/b is an integer and b = 4 is 1 × 1 = 1.
If b = 5, then a = 10 only. So no. of outcomes for which a/b is an integer and b = 5 is 1 × 1 = 1.
There are no possible values of a for which b ≥ 6.
Now the no. of possible outcomes = 9 + 4 + 2 + 1 + 1 = 17.
Hence required probability = 17/90.
Answer:
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