Question

23.

If A, B, C are distinct digits, which of the following numbers cannot be the largest possible 6-digit number
written using three digits A, two digits B, and one digit C?
(A) AAABBC (B) CAAABB (C) BBAAAC (D) AAABCB (E) AAACBB​

Answer 1

The number that cannot be the largest possible 6-digit number is;

(D) AAABCB

Explanation:

From the question, we have;

A, B, and C = Distinct digits, therefore, A ≠ B ≠ C

The number of digits in the number to be formed = 6 digits

The number of 'A' in the number to be formed = 3

The number of 'B' in the number to be formed = 2

The number of 'C' in the number to be formed = 1

We have;

When A > B > C

The largest possible number = AAABBC

When C > A > B

The largest possible number = CAAABB

When B > A > C

The largest possible number = BBAAAC

When A > C > B

The largest possible number = AAACBB

Therefore, given that when A > B > C, the largest possible number = AAABBC, we have;

AAABBC > AAABCB, because B > C, therefore, within the tens and unit of the two 6 digit numbers, we have, BC > CB

∴ AAABBC > AAABCB and AAABCB, cannot be the largest possible 6-digit number