First slide

Introduction to probability

Question

A dice is thrown six times, it being known that each time a different digit is shown. The probability that a sum of 12 will be obtained in the first three throws is

Moderate

A

$\frac{5}{24}$
B

$\frac{25}{216}$
C

$\frac{3}{20}$
D

$\frac{1}{12}$

Solution

Since it is known that each time a different digit appears, total number of cases is 6!
The sum in the first three throws is 12 if we get (1, 5, 6), (2,4,6) or (3 , 4, 5) in any order.
So, number of cases for first three throws = 3 x 3!
The remaining three throws have 3! ways.
$∴$ Number of favourable cases = 3 x 3! x 3!
$∴$ Required probability $= \frac{3 \times 3! \times 3!}{6!} = \frac{3}{20}$

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