How many 4-digit numbers are there with no di | vedclass

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Question

(A) $4$-digit number consists of four places: thousands,hundreds,tens,and units.The thousands place can be filled by any digit from ${1, 2, 3, 4, 5, 6

Vedclass · Accepted Answer

$4536$

Vedclass · Answer

(A) $4$-digit number consists of four places: thousands,hundreds,tens,and units.The thousands place can be filled by any digit from ${1, 2, 3, 4, 5, 6, 7, 8, 9}$. Thus,there are $9$ choices for the thousands place.The hundreds place can be filled by any of the remaining $9$ digits (including $0$,but excluding the digit used in the thousands place). Thus,there are $9$ choices for the hundreds place.The tens place can be filled by any of the remaining $8$ digits. Thus,there are $8$ choices for the tens place.The units place can be filled by any of the remaining $7$ digits. Thus,there are $7$ choices for the units place.By the multiplication principle,the total number of $4$-digit numbers with no digit repeated is $9 	imes 9 	imes 8 	imes 7 = 4536$.

How many $4$-digit numbers are there with no digit repeated?

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