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11 Feb 2021, 07:45
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
61% (02:23) correct
39%
(02:06)
wrong
based on 171
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A five digits number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5, without repetition. What is the total number of ways this can be done?]
(A) 216
(B) 240
(C) 600
(D) 3125
(D) 3325
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
(A) 216
(B) 240
(C) 600
(D) 3125
(D) 3325
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
11 Feb 2021, 08:19
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we have 6 digits and required nos. must be of 5 digits. It means, we can replace only 1 digit.
Sum of digits should be divisible by 3 then the no. will be divisible by 3.
Case1 : To choose from, 5, 4, 3, 2, 1 then 5! = 120 ways
Case 2: To choose from, 5, 4, 0, 2, 1 then 4*4! = 96 ways
So, Total nos. of ways = 120 +96=216
So, I think A.
Sum of digits should be divisible by 3 then the no. will be divisible by 3.
Case1 : To choose from, 5, 4, 3, 2, 1 then 5! = 120 ways
Case 2: To choose from, 5, 4, 0, 2, 1 then 4*4! = 96 ways
So, Total nos. of ways = 120 +96=216
So, I think A.
General Discussion
11 Feb 2021, 08:40
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Here we need a five digit number divisible by 3 (so the sum of the five numbers should be divisible by 3)
So, it can be 0,1,2,4,5 or 1,2,3,4,5
So, it can be done by 5x4x3x2x1 ways for the two sets of numbers.
So, the answer is 2 x (5x4x3x2x1) = 240.
Option: B
So, it can be 0,1,2,4,5 or 1,2,3,4,5
So, it can be done by 5x4x3x2x1 ways for the two sets of numbers.
So, the answer is 2 x (5x4x3x2x1) = 240.
Option: B
