In the New York State daily lottery game, a sequence of 6 (not necessarily different) digits in the range of 0-9 is selected at random.
Find the probability that all 6 are different. Round your answer to four decimal places.

A)0.8488
B) 0.0600
C) 0.3488
D) 0.1512
E) 0.0756

Question

In the New York State daily lottery game, a sequence of 6 (not necessarily different) digits in the range of 0-9 is selected at random. ​
Find the probability that all 6 are different. Round your answer to four decimal places.
​
A)0.8488
B) 0.0600
C) 0.3488
D) 0.1512
E) 0.0756

Quizplus · Accepted Answer

There are a total of $10^6$ possible sequences of 6 digits. If all 6 digits are different, we have 10 choices for the first digit, 9 for the second, and so on, giving a total of $10	imes 9	imes 8	imes 7	imes 6	imes 5$ possible sequences where all digits are different. Therefore, the probability is $\frac{10	imes 9	imes 8	imes 7	imes 6	imes 5}{10^6} = 0.1512$, which is the answer choice D.

In the New York State Daily Lottery Game, a Sequence