Question

The number comprising of more than 5 - digit number​

Answer 1

Answer:

Step-by-step explanation:

We have a 5 digit number. You may visualize the digits as the 5 blanks separated by comma(,) as shown:

_,_,_,_,_

Now these blanks could be filled by either 1 or 2

So, each of the blank space has two choices which may be filled by either 1 or 2

=> we may have 2*2*2*2*2 = 2^5 = 32 different numbers

The smallest of these numbers will be 11111 and the largest will be 22222.

All other 30 numbers will lie between the smallest (11111) & the largest number (22222)

Divisibility of 3 may be ascertained on;ly if the sum of digits is divisible by 3.

The sum of digits for the smallest number having the 5 digits as (1,1,1,1,1) is 5

The sum of digits for the largest number having the 5 digits as (2,2,2,2,2) is 10

The other sums of any such combination will be 6, 7, 8 & 9

Now we know that the only combination leading to a sum of 6 will comprise of four 1’s and one 2. No other combination is possible which gives a sum of 6

Also, the combination leading to a sum of 9 will comprise of four 2’s and one 1. No other combination is possible which gives a sum of 9

So the 5 digits leading to sum of 6 are 1,1,1,1,2 and this combination can be arranged in 5 different ways, simply by exchanging the position of 2 with any 1.

Also the 5 digits leading to sum of 9 are 1,2,2,2,2 and this combination can also be arranged in 5 different ways, simply by exchanging the position of 1 with any 2.

So 5+5 = 10 number out of the 32 possible 5 digit numbers consisting of only 1’s and 2’s are divisible by 3.

Hence 10 is the required answer. Hope this helps