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

Question

The number of 4 digit numbers without repetition that can be formed by using the digits 1,2,3,4,5,6,7 in which each number has two odd digits and two even digits is (A) 432 (B) 436 (C) 450 (D) 454

Tardigrade Admin · Accepted Answer

Two even digits select 3 C 2 ways and two odd digits select 4C2 ways. 4 digit numbers can arrange 4 ! Ways. Thus, required no.of 4 digit numbers =3 C2 × 4 C2 × 4 !=432

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

432

436

450

454

Two even digits select $^{3} C_{2}$ ways and two odd digits select $^{4} C_{2}$ ways.
$4$ digit numbers can arrange $4!$ Ways.
Thus, required no.of $4$ digit numbers $= 3 C_{2} \times 4 C_{2} \times 4! = 432$

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

432

436

450

454

Two even digits select 3C2​ ways and two odd digits select 4C2​ ways. 4 digit numbers can arrange 4! Ways. Thus, required no.of 4 digit numbers =3C2​×4C2​×4!=432

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

Two even digits select $^{3} C_{2}$ ways and two odd digits select $^{4} C_{2}$ ways.
$4$ digit numbers can arrange $4!$ Ways.
Thus, required no.of $4$ digit numbers $= 3 C_{2} \times 4 C_{2} \times 4! = 432$