The number of seven-digit odd numbers that ca | vedclass

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(B) The given digits are $1, 2, 2, 2, 3, 3, 5$. Total digits $= 7$.For a number to be odd,the unit digit must be $1, 3,$ or $5$.Case $1$: Unit digit i

Vedclass · Accepted Answer

$240$

Vedclass · Answer

(B) The given digits are $1, 2, 2, 2, 3, 3, 5$. Total digits $= 7$.For a number to be odd,the unit digit must be $1, 3,$ or $5$.Case $1$: Unit digit is $5$.The remaining digits are $1, 2, 2, 2, 3, 3$. The number of arrangements is $\frac{6!}{3!2!} = \frac{720}{6 	imes 2} = 60$.Case $2$: Unit digit is $3$.The remaining digits are $1, 2, 2, 2, 3, 5$. The number of arrangements is $\frac{6!}{3!} = \frac{720}{6} = 120$.Case $3$: Unit digit is $1$.The remaining digits are $2, 2, 2, 3, 3, 5$. The number of arrangements is $\frac{6!}{3!2!} = \frac{720}{6 	imes 2} = 60$.Total odd numbers $= 60 + 120 + 60 = 240$.

The number of seven-digit odd numbers that can be formed using all the seven digits $1, 2, 2, 2, 3, 3, 5$ is $.......$

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