A middle school assigned a four digit ID number to each student. The number is made from the digits 123 and four and no digit is repeated if assigned randomly, what is the probability that an ID number will end with the number three

Question
Factors and multiples
asked 2020-11-03
A middle school assigned a four digit ID number to each student. The number is made from the digits 123 and four and no digit is repeated if assigned randomly, what is the probability that an ID number will end with the number three

Answers (1)

2020-11-04
If the last digit must be a 3 and no digit can repeat, then there are 3 options (1, 2, and 4) for the first digit, 2 options for the second digit, 1 option for the third digit, and 1 option (a 3) for the last digit. The total number of outcomes that end with the number three is then \(\displaystyle{3}\times{2}\times{1}\times{1}={6}.\)
The total number of possible outcomes is \(\displaystyle{4}\times{3}\times{2}\times{1}={24}\) since there are 4 options for the first digit, 3 for the second, 2 for the third, and 1 for the fourth.
The probability an ID number will end with the number three is then PSK\frac{6}{24}=\frac{1}{4}
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