How many numbers less than 10000 can be forme | vedclass

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(B) Numbers less than $10000$ can have $1, 2, 3,$ or $4$ digits.$1$-digit numbers: The digit can be $1, 2, 3, 4, 5, 6, 7$ (since $0$ is not considered

Vedclass · Accepted Answer

$4095$

Vedclass · Answer

(B) Numbers less than $10000$ can have $1, 2, 3,$ or $4$ digits.$1$-digit numbers: The digit can be $1, 2, 3, 4, 5, 6, 7$ (since $0$ is not considered a $1$-digit number in this context). Total $= 7$.$2$-digit numbers: The first place can be filled in $7$ ways $(1-7)$ and the second place in $8$ ways $(0-7)$. Total $= 7 	imes 8 = 56$.$3$-digit numbers: The first place can be filled in $7$ ways,and the second and third places in $8$ ways each. Total $= 7 	imes 8 	imes 8 = 448$.$4$-digit numbers: The first place can be filled in $7$ ways,and the remaining three places in $8$ ways each. Total $= 7 	imes 8 	imes 8 	imes 8 = 3584$.Total numbers $= 7 + 56 + 448 + 3584 = 4095$.

How many numbers less than $10000$ can be formed using the eight digits $1, 2, 3, 4, 5, 6, 7, 0$? (Repetition of digits is allowed)

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