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

Answer: (B)

Given digits are 1, 2, 3, 4, 5, 6, 7.
Two even digits can be selected in ${}^3{C}_2$
Two odd digits can be selected in ${}^4{C}_2$ ways.
These selected 4 digits can be arranged in 4! ways.
$\therefore Totalnumberofways{=}^4{C}_2{.}^3{C}_2.4!$
$=6\times 3\times 24$
$=18\times 24$
$=432$