The number of integers greater than a million | vedclass

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Question

(C) number greater than a million must have $7$ digits. The given digits are $0, 2, 2, 3, 3, 3, 4$ (total $7$ digits).Since the number must be greater

Vedclass · Accepted Answer

$360$

Vedclass · Answer

(C) number greater than a million must have $7$ digits. The given digits are $0, 2, 2, 3, 3, 3, 4$ (total $7$ digits).Since the number must be greater than a million,the first digit cannot be $0$.Case $1$: The first digit is $2$. The remaining $6$ digits are $0, 2, 3, 3, 3, 4$. The number of arrangements is $\frac{6!}{3!} = \frac{720}{6} = 120$.Case $2$: The first digit is $3$. The remaining $6$ digits are $0, 2, 2, 3, 3, 4$. The number of arrangements is $\frac{6!}{2!2!} = \frac{720}{4} = 180$.Case $3$: The first digit is $4$. The remaining $6$ digits are $0, 2, 2, 3, 3, 3$. The number of arrangements is $\frac{6!}{2!3!} = \frac{720}{12} = 60$.Total number of integers = $120 + 180 + 60 = 360$.

The number of integers greater than a million that can be formed using the digits $2, 3, 0, 3, 4, 2, 3$ is:

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