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  • The total number of three digit numbers,with one digit repeated exactly two times, is ________Option: 1 243<str

The total number of three digit numbers,with one digit repeated exactly two times, is ________

Option: 1

243


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

since three digit number can not start with 0 at hundred's place, therefore number of ways to write it will be = 9_{c_{1}} \times 2

later, for remaining non zero digits taken two at a time can be written in 9_{c_{1}} \times 1 ways

now, the other ways of making three digit numbers can be written in 9_{c_{2}} \times{ 2}_{c_{1}} and finally as there is repetition of two numbers in three digit number the total possible ways will be multiplied by \frac{3 !}{2 !}

\mathrm{0 a a+100 a+a a b \text { or } a b b}

\mathrm{9_{c_{1}} \times 2+9_{c_{1}} \times 1+9_{c_{2}} \times{ 2}_{c_{1}} \times \frac{3 !}{2 !}}

\mathrm{18+9+216}\\

\mathrm{=243}

Hence the answer is \mathrm{243}

Posted by

Sanket Gandhi

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