Question

The number of $4$ digit numbers without repetition that can be formed using the digits $1,2,3,4,5,6,7$ in which each number has two odd digits and two even digits is

• A. $450$
• B. $432$
• C. $454$
• D. $436$

Answer 1

The correct option is B $432$

Odd digits $=1,3,5,7$
Even digits $=2,4,6$
Two odd digits can be selected in ${}^4{C}_2$ ways and two even digits can be selected in ${}^3{C}_2$ ways.
Again, these 4 digits can be arranged in $4!$ ways.
$\therefore$ No. of digits formed ${=}^4{C}_2{\times }^3{C}_2\times 4!=432$