Permutations & Combinations
5-digit numbers from given digits; divisibility by 6
MMTS_Full_Test_22
Grade 12
Question:
Number of natural numbers with 5 distinct digits formed using $\{1,2,3,5,6,7,9\}$ and divisible by 6 are
(A) 72
(B) 192
(C) 216
(D) 240
Step-by-Step Solution
Key Concept: Divisible by 6 = divisible by 2 and 3. Units digit must be from $\{2,6\}$. Sum of 5 chosen digits divisible by 3.
240 numbers.
Correct Answer: (D) 240