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Question

Five digits numbers are formed using the digits 1,2,3,4,5,6 and 8. What is the probability that has even digits at both the ends?


A

27

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B

37

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C

47

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D

None of these

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Solution

The correct option is A

27


An explanation for the correct option:

Step 1: Find the number of possible outcomes for a given event.

We have been given the five digits numbers are formed using the digits 1,2,3,4,5,6 and 8.

We need to find the probability that has even digits at both ends.

The five digits numbers are formed using the digits 1,2,3,4,5,6 and 8.

The total number of possible cases would be,

⇒n(S)=P57⇒n(S)=7!(7-5)!⇒n(S)=2520

Let event A: the five-digit number has even digits at both ends.

The number of ways to form the numbers which have even digits at both the ends would be,

⇒n(A)=4×3×P35⇒n(A)=4×3×5!(5-3)!⇒n(A)=4×3×60⇒n(A)=720

Step 2: Find the required probability.

Using the formula of probability the required probability would be,

⇒P(A)=n(A)n(S)⇒P(A)=7202520⇒P(A)=27

Therefore, option (A) is the correct answer.


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