Question

In a New York State daily lottery game, a sequence of five digits (not necessarily different) in the range 0-9 are selected at random. Find the probability that all five are different.

Answer 1

Answer: Our required probability is 0.30.

Step-by-step explanation:

Since we have given that

Number we have 0 to 9 = 10

Number of digits = 5

Total number of outcomes = $10^5=10000$

All 5 are different.

So, the number of ways selecting all 5 are different is given by

$^{10}C_5\times 5!=30240$

So, probability that all five are different is given by

$\dfrac{30240}{10000}\\\\=0.30240\\\\\approx 0.30$

Hence, our required probability is 0.30.