Question
How many numbers greater than $24000$ can be formed by using digits $1, 2, 3, 4, 5 $when no digit is repeated
Required number will be = (Total) -(Those beginning with $1$) -(Those beginning with $21$) -(Those beginning with $23$)
= $5\,!\, - \,4\,!\, - 3\,!\, - 3\,!\, = \,120 - 24 - 6 - 6 = 84$.
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$I_n=\int_0^1\left(1-x^k\right)^n d x, n \in \mathbb{N} \text {, satisfies } 147 I_{20}=148 I_{21}$ is :
