Count the numbers that can be formed by the digits 0, 3, 4 and 8 which

1.	Count the numbers that can be formed by the digits 0, 3, 4 and 8 which is divisible by 5. The number must range between 100 to 100000 (both inclusive) and digits can be repeated.1. 1422. 2043. 2734. 117
Answer» Correct Answer - Option 4 : 117 Concept: The ways of arranging n different things = n! The ways of arranging n things, having r same things and rest all are different = \(\rm n!\over r!\) The no. of ways of arranging the n arranged thing and m arranged things together = n! × m! The number of ways for selecting r from a group of n (n > r) = nCr Calculation: For a number to be divisible by 5 only if the number end with 0 or 5, here the case is 0, hence the unit digit has to be 0. Now, remaining are 3 digits 3, 4 and 8 If the number is between (101 and 999), the ways = 3²× 1 = 9 If the number is between (1000 and 9999), the ways = 33 × 1 = 27 If the number is between (10000 and 99999), the ways = 34 × 1 = 81 ∴ Total number of ways = 9 + 27 + 81 Total number = 117

Count the numbers that can be formed by the digits 0, 3, 4 and 8 which is divisible by 5. The number must range between 100 to 100000 (both inclusive) and digits can be repeated.1. 1422. 2043. 2734. 117

Answer» Correct Answer - Option 4 : 117

Concept:

The ways of arranging n different things = n!
The ways of arranging n things, having r same things and rest all are different = \(\rm n!\over r!\)
The no. of ways of arranging the n arranged thing and m arranged things together = n! × m!
The number of ways for selecting r from a group of n (n > r) = nCr

Calculation:

For a number to be divisible by 5 only if the number end with 0 or 5, here the case is 0, hence the unit digit has to be 0.

Now, remaining are 3 digits 3, 4 and 8

If the number is between (101 and 999), the ways = 3²× 1 = 9

If the number is between (1000 and 9999), the ways = 33 × 1 = 27

If the number is between (10000 and 99999), the ways = 34 × 1 = 81

∴ Total number of ways = 9 + 27 + 81

Total number = 117