The number of integers,greater than 7000,that | vedclass

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Question

(B) To form an integer greater than $7000$ using the digits ${3, 5, 6, 7, 8}$ without repetition,we can form either $4$-digit numbers or $5$-digit num

Vedclass · Accepted Answer

$168$

Vedclass · Answer

(B) To form an integer greater than $7000$ using the digits ${3, 5, 6, 7, 8}$ without repetition,we can form either $4$-digit numbers or $5$-digit numbers.$1$. For $4$-digit numbers:The first digit (thousands place) must be $7$ or $8$ (since the number must be $> 7000$).If the first digit is $7$ or $8$ ($2$ choices),the remaining $3$ positions can be filled by the remaining $4$ digits in $P(4, 3) = 4 	imes 3 	imes 2 = 24$ ways.Total $4$-digit numbers $= 2 	imes 24 = 48$.$2$. For $5$-digit numbers:Since all $5$-digit numbers formed using these $5$ digits are greater than $7000$,the number of such integers is $5! = 120$.Total integers $= 48 + 120 = 168$.

The number of integers,greater than $7000$,that can be formed using the digits $3, 5, 6, 7, 8$ without repetition is:

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