Question

What is the average of all five digit numbers that can be formed using all the digits 1, 2, 3, 4, 5 exactly once?

• A. 33322
• B. 33333
• C. 32235
• D. 33225

Answer 1

The correct option is B 33333

Option(b)

To find the average of all numbers, we need to find the sum of all the possible numbers and divide it by the total such numbers possible.The sum of all possible numbers can be found using the formula

(n-1)!(sum of digits)(1111…n times)

here n=5

(5-1)!(15)(11111)= 4!(15)(11111)

Total number of such possible cases= 5!

Average= 3999960/5! = 33333

Short cut: - If we arrange given numbers, These numbers will be in A.P.

Ao, A.M. of these numbers = (First term + last term)/2

(12345+54321 )/2 = 33333