Question

A 6-digit PIN number is selected. What it the probability that there are no repeated digits?
The probability that no numbers are repeated is
Write your answer in decimal form, rounded to the nearest thousandth.
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Answer 1

Mark Brainliest please

Answer: 0.1512

So I know that there are 10 possible digits that can be selected, each time the pool of selected digits gets smaller.

The first digit cannot be zero therefore there are 9 possibilities for this digit. Then, seeing as the order doesn't matter, but repeats do, so I thought a permutation would be the correct method to apply.

9 * ((9!)/(9-5!)) = 136,080 (<-- total number of 6 digit numbers)

Without repeats and no 0 as first digit

Total number of 6 digit numbers = 10^6

Therefore the probability of this scenario happening is:

(139,080/10000000) = 0.13608

Answer 2

Answer:

we got 10 digits to choose from for the first digit, 9 for the second and so on

$10 \times 9 \times 8 \times 7 \times 6 \times 5$

scenarios that got no repeated digits.

the total number of possible PINs with 6 digits is

$10 \times 10 \times 10 \times 10 \times 10 \times 10$

or just 10⁶

so the fraction we are looking for is the number of valid states decided by all possible states.

$\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5}{ {10}^{6} }$

=0.1512

rounded to the nearest thousandth it's

0.151

(actually, I didn't expect the probability to be around 15 percent)

hope it helps. asked question whenever you like

kind regards

Alex