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A FIVE DIGIT NUMBER IS FORMED BY USING THE DIGITS 1,2,3,4&5 WITH OUT R

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A FIVE DIGIT NUMBER IS FORMED BY USING THE DIGITS 1,2,3,4&5 WITH OUT R  [#permalink]

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New post 08 Oct 2010, 04:49
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A FIVE DIGIT NUMBER IS FORMED BY USING THE DIGITS 1,2,3,4&5 WITH OUT REPETITIONS . WHAT IS THE PROBABILITY THE NUMBER IS DIVISIBLE BY4?

A) 1/5
B) 5/6
C) 4/5
D) 7/3
E) 2/7
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Re: A FIVE DIGIT NUMBER IS FORMED BY USING THE DIGITS 1,2,3,4&5 WITH OUT R  [#permalink]

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New post 08 Oct 2010, 05:15
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anilnandyala wrote:
A FIVE DIGIT NUMBER IS FORMED BY USING THE DIGITS 1,2,3,4&5 WITH OUT REPETITIONS . WHAT IS THE PROBABILITY THE NUMBER IS DIVISIBLE BY4?

A)1/5
B)5/6
C)4/5
D)7/3
E)2/7


P = Number of desired outcomes / number of possible outcomes

Number of desired outcomes:
To be divisible by 4, the number has to end with the last two digits forming a number divisible by 4. Given the numbers in the question this leaves us with:
12
24
32
52
For each of them I now have to put the remaining numbers in front: 3x2x1 --> 6 combinations for each number set = 6x4 (we have 4 sets from above) = 24

Number of possible outcomes:
The total number of possibilities to form a 5 digit number from the question= 5x4x3x2x1=120

P = 24/120 = 1/5 --> A
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Re: A FIVE DIGIT NUMBER IS FORMED BY USING THE DIGITS 1,2,3,4&5 WITH OUT R  [#permalink]

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New post 08 Oct 2010, 10:00
It has to be A. (3!x4/5!) = 1/5
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Re: A FIVE DIGIT NUMBER IS FORMED BY USING THE DIGITS 1,2,3,4&5 WITH OUT R  [#permalink]

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New post 08 Oct 2010, 10:55
arundas wrote:
It has to be A. (3!x4/5!) = 1/5



Please explain your process.
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Re: A FIVE DIGIT NUMBER IS FORMED BY USING THE DIGITS 1,2,3,4&5 WITH OUT R  [#permalink]

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New post 09 Oct 2010, 11:49
Baten80 wrote:
arundas wrote:
It has to be A. (3!x4/5!) = 1/5



Please explain your process.


***12 stars can be filled in 3! ways
***24 stars can be filled in 3! ways
***32 stars can be filled in 3! ways
***54 stars can be filled in 3! ways

So total option multiple of 4 = 4*3!

Total options = 5!

So prob. = 4*3!/5!
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Re: A FIVE DIGIT NUMBER IS FORMED BY USING THE DIGITS 1,2,3,4&5 WITH OUT R  [#permalink]

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New post 10 Oct 2010, 03:07
the ans is 24/120 = 1/5
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Re: A FIVE DIGIT NUMBER IS FORMED BY USING THE DIGITS 1,2,3,4&5 WITH OUT R  [#permalink]

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New post 08 Jun 2016, 23:39
A 5-digit number is formed by the numbers 1, 2, 3, 4 and 5, without repetition. What is the probability that the number formed is a multiple of 4 ?

A) 1/4
B) 3/5
C) 2/5
D) 4/5
E) 1/5


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Re: A FIVE DIGIT NUMBER IS FORMED BY USING THE DIGITS 1,2,3,4&5 WITH OUT R  [#permalink]

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New post 09 Jun 2016, 00:06
Topic Merged. Rules for posting: rules-for-posting-please-read-this-before-posting-133935.html#p1092822

If a number is divisible by 4 the last 2 digits of the number has to be divisible by 4.

If the number ends with 12: Number of possibilities = 3 * 2 * 1 = 6
number ends with 24: Possibilities = 3 * 2 * 1 = 6
number ends with 32: Possibilities = 6
number ends with 52: Possibilities = 6

Total number of possibilities with restriction = 6 + 6 + 6 + 6 = 24
Total number of possibilities without restriction = 5! = 120

Probability = 24/120 = 1/5

Answer: E
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Re: A FIVE DIGIT NUMBER IS FORMED BY USING THE DIGITS 1,2,3,4&5 WITH OUT R  [#permalink]

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New post 15 Jun 2019, 13:55
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Re: A FIVE DIGIT NUMBER IS FORMED BY USING THE DIGITS 1,2,3,4&5 WITH OUT R   [#permalink] 15 Jun 2019, 13:55
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