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
$(1989,2 M)$
(a) 216
(b) 240
(c) 600
(d) 3125
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Answer:
Correct Answer: 8. (a)
Solution:
- Since, a five-digit number is formed using the digits ${0,1,2,3,4$ and 5$}$ 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 $=4 \times 4 \times 3 \times 2 \times 1=96$
Case II Using digits $1,2,3,4,5$
Number of ways $=5 \times 4 \times 3 \times 2 \times 1=120$
$\therefore$ Total numbers formed $=120+96=216$
