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)

432

Answer 2

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.
$\therefore\, Total \,number\, of \,ways=^{4}C_{2}. ^{3}C_{2}. 4!$
$=6\times3\times24$
$=18\times24$
$=432$