Two numbers 'a ’ and '6 ’ are selected successively without repla… - Vidyadip

MCQ

Two numbers $'a\ ’$ and $'6\ ’$ are selected successively without replacement in that order from the integers $1$ to $10$. The probability that $\frac{\text{a}}{\text{b}}$ is an integer, is :

A
$\frac{17}{45}$
B
$\frac{1}{5}$
✓
$\frac{17}{90}$
D
$\frac{8}{45}$

✓

Answer

Correct option: C.

$\frac{17}{90}$

$a$ and $b$ are two number to be selected from the integers $= 1$ to $10$ without replacement of $a$ and $b$
i.e., $1$ to $10 = 10$
And $2$ to $10 = 9$
No. of ways $= 10 \times 9 = 90$
Probability of $\frac{\text{a}}{\text{b}}$ where it is an integer
Possible event will be $= \{(2, 2), (3, 3)\},$
$\{(4, 2), (4, 4), (5, 5)\},$
$\{(6, 2), (6, 3), (6, 6),(7, 7), (8, 2), (8, 4), (8, 8),\}$
$\{(9, 3), (9, 9), (10, 2), (10, 5), (10, 10)\}, = 17$
$\text{P(E)}=\frac{\text{m}}{\text{n}}=\frac{17}{90}$

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