The number of six digit numbers that can be formed using the digits 0, 1, 2, 3, 4, 5, 6 so that digits do not repeat and the first and last place are even, is

Question

The number of six digit numbers that can be formed using the digits 0, 1, 2, 3, 4, 5, 6 so that digits do not repeat and the first and last place are even, is (A) 1080 (B) 1440 (C) 1220 (D) 720

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/144221a4ef49bc1c74249276cab1a97c-.png" /> Case-I: When ' 0 ' is not at terminal position 3 C 2 ⋅ 2 ! ⋅ 5 C 4 ⋅ 4 !=6 × 120=720 Case-II: When 0 is at last place 3 C 1 ⋅ 1 ⋅ 5 C 4 ⋅ 4 !=3 × 120=360 Total number of six digit numbers =720+360=1080.

Q. The number of six digit numbers that can be formed using the digits $0, 1, 2, 3, 4, 5, 6$ so that digits do not repeat and the first and last place are even, is

1080

1440

1220

720

Case-I: When ' 0 ' is not at terminal position
$^{3} C_{2} \cdot 2! \cdot^{5} C_{4} \cdot 4! = 6 \times 120 = 720$
Case-II: When 0 is at last place
$^{3} C_{1} \cdot 1 \cdot^{5} C_{4} \cdot 4! = 3 \times 120 = 360$
Total number of six digit numbers $= 720 + 360 = 1080$ .

Q. The number of six digit numbers that can be formed using the digits 0,1,2,3,4,5,6 so that digits do not repeat and the first and last place are even, is

1080

1440

1220

720

Case-I: When ' 0 ' is not at terminal position 3C2​⋅2!⋅5C4​⋅4!=6×120=720 Case-II: When 0 is at last place 3C1​⋅1⋅5C4​⋅4!=3×120=360 Total number of six digit numbers =720+360=1080.

Q. The number of six digit numbers that can be formed using the digits $0, 1, 2, 3, 4, 5, 6$ so that digits do not repeat and the first and last place are even, is

Case-I: When ' 0 ' is not at terminal position
$^{3} C_{2} \cdot 2! \cdot^{5} C_{4} \cdot 4! = 6 \times 120 = 720$
Case-II: When 0 is at last place
$^{3} C_{1} \cdot 1 \cdot^{5} C_{4} \cdot 4! = 3 \times 120 = 360$
Total number of six digit numbers $= 720 + 360 = 1080$ .