If a 3-digit number is formed from the digits 1—5 without repetition, what is the probability the number is divisible by 5?

Rationale

The probability that a 3-digit number formed from the digits 1—5 without repetition is divisible by 5 is 1/5.

To determine this probability, we first recognize that a 3-digit number is divisible by 5 if its last digit is 5. Given the digits 1 through 5, we can form multiple combinations, but only numbers ending in 5 will meet the divisibility requirement.

A (1/10) YOUR ANSWER

This choice suggests that there is only one valid outcome for every ten possible outcomes, which is not accurate in this scenario. The total number of 3-digit combinations from the digits 1—5 is 60 (5 choices for the first digit, 4 for the second, and 3 for the last), and with 12 of these ending in 5, this fraction does not correctly represent the situation.

B (1/5) CORRECT

When the last digit is fixed as 5, the first two digits can be any of the remaining four digits (1, 2, 3, or 4), which provides 12 favorable outcomes (4 choices for the first digit and 3 for the second). Therefore, the probability is 12 out of 60 total combinations, simplifying to 1/5, confirming that this choice is correct.

C (1/4) YOUR ANSWER

This option implies that 15 out of 60 combinations are divisible by 5, which is incorrect. The actual number of combinations that meet the divisibility condition is only 12, making this probability overstated.

D (2/5) YOUR ANSWER

This choice suggests that 24 out of 60 combinations are divisible by 5, which again is incorrect. Only 12 combinations are divisible by 5, thus this fraction is an overestimation of the valid outcomes.

E (1/2) YOUR ANSWER

This option posits that half of the combinations are divisible by 5, which is not the case. Out of 60 total combinations, only 12 are valid, meaning this choice significantly overstates the probability.

Conclusion

The calculation of the probability that a randomly formed 3-digit number from the digits 1—5 is divisible by 5 results in 1/5. This is derived from the limited number of valid combinations where 5 is the last digit, confirming that the other choices inaccurately represent the true likelihood of divisibility. The correct understanding of favorable versus total outcomes is essential for determining accurate probabilities in combinatorial problems.

If a 3-digit number is formed from the digits 1—5 without repetition, what is the probability the number is divisible by 5?

The probability that a 3-digit number formed from the digits 1—5 without repetition is divisible by 5 is 1/5.

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