Question

B. How many 4-digit numbers that can be formed using the digits 2, 3, 4, 6,7, 8 which are divisible by 6, if no digit occurs more than once in each number?
78
56
84
112​

Answer 1

answer .370

We need to find 4 digit numbers that are divisible by 4 ξ contain numbers 0 to 7.

Since the number is to be divisible by 4 the last 2 digits can only be one of the following:

1).12,16,24,32,36,52,56,64,72,76

2).20,40,60,04

For set 1). There are 10 possible ways for last 2 digits. For the first digit 0 cannot be used and also the 2 digits already used for last 2 digits. So we have (8−3)=5 choices for 1st digit and then again 5 remaining choices for 2nd digit.

⇒ Total =10×5×5

=250.

For set 2). Last 2 digits can be chosen from 4 possibilities. First 2 digits can be chosen from remaining 6 numbers.

⇒ Total =4×

6

P

2

=4×30

=120.

⇒ Required =250+120

=370.