Permutations and Combinations 1 Question 8

8. A five digits number divisible by 3 is to be formed using the numbers 0,1,2,3,4 and 5 , without repetition. The total number of ways this can be done, is

(1989,2M)

(a) 216

(b) 240

(c) 600

(d) 3125

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Answer:

Correct Answer: 8. (a)

Solution:

  1. Since, a five-digit number is formed using the digits 0,1,2,3,4$and5$ divisible by 3 i.e. only possible when sum of the digits is multiple of three. Case I Using digits 0,1,2,4,5

Number of ways =4×4×3×2×1=96

Case II Using digits 1,2,3,4,5

Number of ways =5×4×3×2×1=120

Total numbers formed =120+96=216



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