The number of different 6-digit numbers that | vedclass

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(B) number is divisible by $10$ if and only if its unit's digit is $0$.Given digits are ${1, 2, 7, 0, 9, 5}$.To form a $6$-digit number,we have $6$ po

Vedclass · Accepted Answer

$120$

Vedclass · Answer

(B) number is divisible by $10$ if and only if its unit's digit is $0$.Given digits are ${1, 2, 7, 0, 9, 5}$.To form a $6$-digit number,we have $6$ positions to fill.Since the number must be divisible by $10$,the unit's place must be occupied by $0$. This leaves $1$ choice for the unit's place.The remaining $5$ positions can be filled by the remaining $5$ digits ${1, 2, 7, 9, 5}$ in $5!$ ways.Number of ways $= 5! = 5 	imes 4 	imes 3 	imes 2 	imes 1 = 120$.Therefore,the total number of such $6$-digit numbers is $120$.

The number of different $6$-digit numbers that are divisible by $10$,which can be formed using the digits $1, 2, 7, 0, 9, 5$?

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