Permutations and Combinations – JEE Main 24 January 2025 Shift 1

Question ID: #384
JEE Main24 January Shift 1, 2025Algebra

The number of 3-digit numbers, that are divisible by 2 and 3, but not divisible by 4 and 9, is


    Solution:


    Total number of 3-digit numbers = $999 – 99 = 900$.

    Number of 3-digit numbers divisible by 2 and 3 (i.e., divisible by 6):
    $$ \frac{900}{6} = 150 $$

    Number of 3-digit numbers divisible by 4 and 9 (i.e., divisible by 36):
    $$ \frac{900}{36} = 25 $$

    Therefore, the number of 3-digit numbers divisible by 2 and 3 but not by 4 and 9 is:
    $$ 150 – 25 = 125 $$

    Ans. (125)

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