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Q.
The number of $3$ digit numbers, that are divisible
by either $3$ or $4$ but not divisible by $48$, is
JEE MainJEE Main 2023Permutations and Combinations
Solution:
Total 3 digit number $=900$
Divisible by $3=300$
(Using $\frac{900}{3}=300$ )
Divisible by $4=225$
(Using $\frac{900}{4}=225$ )
Divisible by $3$ & $4=108, \ldots$.
(Using $\frac{900}{12}=75$ )
Number divisible by either 3 or 4
$=300+2250-75=450$
We have to remove divisible by $48$ ,
$144,192, \ldots ., 18$ terms
Required number of numbers $=450-18=432$