GODSPEED wrote:

In how many ways can 3-digit numbers be formed selecting 3 digits from 1, 1, 2, 3, 4?

A. 5P3/(2!)

B. 4P3

C. 4^3

D. 4P3+3C1*(3!/2!)

E. 60 × 3!

We will separate the 3-digit numbers into two types: Those that contain two 1s and those that contain at most one 1.

1) The numbers that contain two 1s:

These numbers will be of the form _11, 1_1, or 11_, where _ is a digit of 2, 3, or 4. So, there are a total of 9 such numbers.

2) The numbers that contain at most one 1:

These numbers will consist of 3 of the digits 1, 2, 3, and 4. Since the order is important, there are 4P3 such numbers.

Scanning the answer choices, we see that D is the correct answer.

Answer: D

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