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(C) The given digits are $1, 2, 3, 4, 5$. We need to form $5$-digit numbers greater than $24000$.Total $5$-digit numbers possible without repetition i

Vedclass · Accepted Answer

$84$

Vedclass · Answer

(C) The given digits are $1, 2, 3, 4, 5$. We need to form $5$-digit numbers greater than $24000$.Total $5$-digit numbers possible without repetition is $5! = 120$.Numbers starting with $1$ (i.e.,$1xxxx$) = $4! = 24$.Numbers starting with $21$ (i.e.,$21xxx$) = $3! = 6$.Numbers starting with $23$ (i.e.,$23xxx$) = $3! = 6$.Numbers starting with $24000$ are not possible since $0$ is not in the set.Numbers starting with $24$ (i.e.,$24xxx$) where $x > 0$: The remaining digits are ${1, 3, 5}$. The numbers are $24135, 24153, 24315, 24351, 24513, 24531$. There are $3! = 6$ such numbers.Total numbers greater than $24000$ = (Total numbers) - (Numbers starting with $1$) - (Numbers starting with $21$) - (Numbers starting with $23$) = $120 - 24 - 6 - 6 = 84$.

How many numbers greater than $24000$ can be formed by using the digits $1, 2, 3, 4, 5$ when no digit is repeated?

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