How many numbers greater than 24000 can be fo | vedclass

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

Vedclass · Accepted Answer

$84$

Vedclass · Answer

(C) The digits available 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 $1$ are $4! = 24$.Numbers starting with $21$ are $3! = 6$.Numbers starting with $23$ are $3! = 6$.Numbers starting with $24$ are $2! = 2$ (these are $24135$ and $24153$,both are $> 24000$).Alternatively,using the subtraction method:Total numbers = $120$.Numbers $\le 24000$ are:- Starting with $1$: $4! = 24$.- Starting with $21$: $3! = 6$.- Starting with $23$: $3! = 6$.Total numbers $\le 24000$ is $24 + 6 + 6 = 36$.Numbers $> 24000 = 120 - 36 = 84$.

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

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