Q59 / 160 · TS EAMCET 2023 (13 May Shift 2) · Mathematics

All possible 5 digit numbers each having 5 distinct digits are formed using digits $1,2,3,5,6,8$. Among them, the number of numbers which are divisible by 3 but not by 6 is

A
120
B
72
Correct answer
C
48
D
240

Solution

$1,2,3,5,6,8$ To form number divisible by 3 , they must contain $(2,3,5,6,8)$ and if it is not divisible by 6 , hence it must be odd. $\overline{4} \times \overline{3} \times \overline{2} \times \overline{1} \times \overline{2}=4 ! \times 2$ ways $=48$ ways

Hence, the correct answer is option: 'C'.

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