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In how many ways can 3-digit numbers be formed selecting 3 d

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Re: In how many ways can 3-digit numbers be formed selecting 3 d [#permalink]

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New post 13 Aug 2017, 21:04
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Re: In how many ways can 3-digit numbers be formed selecting 3 d [#permalink]

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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!


Given digits : 1,1,2,3,4
There can be 2 cases for forming 3 digit numbers.

Case 1 : When 1 is used only once and we need to form the 3-digit number from digits 1,2,3,4 (Nos. like 123,234, etc.)
No. of such numbers = 4P3

Case 2 : When 1 is used twice and 3rd digit is taken from 2,3,4 (Nos. like 113,141, etc.)
No. of such numbers = 3C1*3!/2! (3C1 for selecting one number out of 3 numbers 2,3,4; 3! means arranging the 3 numbers 1,1 and 3rd selected number and it is divided by 2! as there are 2 1's. Due to which many numbers will be similar.)

Total numbers : 4P3 + 3C1*3!/2!

Answer D
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Re: In how many ways can 3-digit numbers be formed selecting 3 d [#permalink]

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New post 18 Aug 2017, 08:06
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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Re: In how many ways can 3-digit numbers be formed selecting 3 d [#permalink]

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New post 19 Aug 2017, 05:12
I am also getting answer C as question does not mention that repetition is not allowed

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Re: In how many ways can 3-digit numbers be formed selecting 3 d   [#permalink] 19 Aug 2017, 05:12

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