(B) number is divisible by $4$ if the number formed by its last two digits is divisible by $4$. The available digits are $\{0, 1, 2, 3, 4\}$.For a $4$

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(B) number is divisible by $4$ if the number formed by its last two digits is divisible by $4$. The available digits are $\{0, 1, 2, 3, 4\}$.For a $4$-digit number $d_1 d_2 d_3 d_4$,$d_1 \in \{1, 2, 3, 4\}$ ($4$ choices),$d_2 \in \{0, 1, 2, 3, 4\}$ ($5$ choices).The last two digits $d_3 d_4$ must form a number divisible by $4$. Possible pairs $(d_3, d_4)$ are:$00, 04, 12, 20, 24, 32, 40, 44$.There are $8$ such pairs.Total numbers $= 4 \times 5 \times 8 = 160$.

Class 11 Mathematics Permutations and Combinations Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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Among the $4$-digit numbers formed using the digits $0, 1, 2, 3, 4$ where repetition of digits is allowed,the number of numbers which are divisible by $4$ is:

AP EAMCET 2024 All AP EAMCET

A
$140$
B
$160$
C
$180$
D
$200$

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Permutations and Combinations

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Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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