How many 4-digit numbers are there with disti | vedclass

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(A) To form a $4$-digit number with distinct digits,we have $4$ positions: thousands,hundreds,tens,and units.$1$. For the thousands place,we cannot us

Vedclass · Accepted Answer

$4536$

Vedclass · Answer

(A) To form a $4$-digit number with distinct digits,we have $4$ positions: thousands,hundreds,tens,and units.$1$. For the thousands place,we cannot use $0$. Therefore,we have $9$ choices $(1, 2, 3, 4, 5, 6, 7, 8, 9)$.$2$. For the hundreds place,we can use $0$,but we cannot use the digit already placed in the thousands place. Thus,we have $9$ choices ($0$ plus the $8$ remaining digits).$3$. For the tens place,we cannot use the $2$ digits already placed. Thus,we have $8$ choices.$4$. For the units place,we cannot use the $3$ digits already placed. Thus,we have $7$ choices.Total number of $4$-digit numbers with distinct digits $= 9 	imes 9 	imes 8 	imes 7 = 4536$.

How many $4$-digit numbers are there with distinct digits?

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