(B) Numbers divisible by $5$ must have $5$ in the units place.Case $1$: $3$-digit numbers.The units place is fixed as $5$. The remaining $2$ places ca

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(B) Numbers divisible by $5$ must have $5$ in the units place.Case $1$: $3$-digit numbers.The units place is fixed as $5$. The remaining $2$ places can be filled by the remaining $3$ digits $(3, 4, 6)$ in $^3P_2 = 3 \times 2 = 6$ ways.Case $2$: $4$-digit numbers.The units place is fixed as $5$. The remaining $3$ places can be filled by the remaining $3$ digits $(3, 4, 6)$ in $^3P_3 = 3 \times 2 \times 1 = 6$ ways.Total numbers $= 6 + 6 = 12$.

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

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How many numbers greater than $100$ and divisible by $5$ can be made from the digits $3, 4, 5, 6$,if no digit is repeated?

A
$6$
B
$12$
C
$24$
D
$30$

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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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The sum of all numbers formed by using all the digits $3, 1, 7, 9$ exactly once is:

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How many numbers greater than $100$ and divisible by $5$ can be made from the digits $3, 4, 5, 6$,if no digit is repeated?

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All words,with or without meaning,are made using all the letters of the word $MONDAY$. These words are written as in a dictionary with serial numbers. The serial number of the word $MONDAY$ is

The number of five-digit numbers,greater than $40000$ and divisible by $5$,which can be formed using the digits $0, 1, 3, 5, 7,$ and $9$ without repetition,is equal to:

If the letters of the word $MATHS$ are permuted and all possible words so formed are arranged as in a dictionary with serial numbers,then the serial number of the word $THAMS$ is

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