The number of numbers,strictly between 5000 a | vedclass

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Question

(D) To form a number strictly between $5000$ and $10000$,the number must be a $4$-digit number.The first digit (thousands place) must be greater than

Vedclass · Accepted Answer

$72$

Vedclass · Answer

(D) To form a number strictly between $5000$ and $10000$,the number must be a $4$-digit number.The first digit (thousands place) must be greater than or equal to $5$. Given the set of digits $\{1, 3, 5, 7, 9\}$,the possible choices for the thousands place are $5, 7, 9$ ($3$ choices).Since repetition is not allowed,we have $4$ remaining digits for the hundreds place,$3$ remaining digits for the tens place,and $2$ remaining digits for the units place.Total numbers $= 3 	imes 4 	imes 3 	imes 2 = 72$.

The number of numbers,strictly between $5000$ and $10000$,that can be formed using the digits $1, 3, 5, 7, 9$ without repetition is $..........$.

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