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  • Without repetition of the numbers, four digit numbers are formed with the numbers 0, 2, 3, 5. The probability of such a number divisible by 5 is A. 1 / 5 B. 4 / 5 C. 1 /30 D. 5 / 9

Without repetition of the numbers, four digit numbers are formed with the numbers 0, 2, 3, 5. The probability of such a number divisible by 5 is

A. 1/5

B. 4/5

C. 1/30

D. 5/9

Answers (1)

Given digits: 0, 2, 3, 5

Now, we now that if a no. is divisible by 5, then the digit in the units place should be either 0 or 5

Now, if units place is 0, then

3

2

1

1

 Now, the first three places can be filled in 3! Ways

= 3 x 2 x 1 x 1

= 6

Now, if units place is 5, then,

2

1

1

1

 Here, we can fill the first two places in 2 ways & the 2nd and 3rd place in 2! Ways

= 2 x 2 x 1 x 1

= 4

  Thus, the total no. of ways = 6 + 4

                                                = 10

                                                = n (E)

Now, total no. of ways to arrange the given digits to form 4 – digits without repetition is 3 x 3 x 2 x 1

= 18

Probability = no. of favorable outcomes/ total no. of outcomes

                        = 10 /18

                        = 5 /9

Thus, option D is the correct answer.

Posted by

infoexpert22

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