Question

The number of different seven digit numbers that can be written using only three digits 1, 2 & 3 under the condition that the digit 2 occurs exactly twice in each number is-

• A. 672
• B. 640
• C. 512
• D. None of these

Answer 1

The correct option is A 672

choose any two of the seven digit

This may be done in ${}^7{C}_2$ ways

put 2 in these two digits .

The remaining 5 digit may be arranged

using 1 and 3 in $2^5$ ways.

so, squired numbers of numbers

=${}^7{C}_2\times 2^5$

=$\frac{7!}{5!2!}\times 2^5$

=$\frac{7\times 6\times 5!}{5!\times 2}\times 2^5$

=$21\times 32=672$