All AnswersA 4-letter code word consists of letters A, B, and C. If the code includes all the three letters, how many such codes are possible?
Asked by Keerti Taneja 10 months ago
A 4-letter code word consists of letters A, B, and C. If the code includes all the three letters, how many such codes are possible?
We need to form a 4-letter code using A, B, and C, and it must include all three letters.
Let's consider the arrangements of the letters:
We must have one of the letters repeated.
Case 1: The repeated letter is A.
Possible arrangements: AABC, AACB, ABAA, ABCA, ACAA, AABC, ACAB, ACBA
Case 2: The repeated letter is B.
Possible arrangements: BABC, BACB, BBAA, BBCA, BCAA, BABC, BCAB, BCBA
Case 3: The repeated letter is C.
Possible arrangements: CABC, CACB, CBAA, CBCA, CBAA, CABC, CABCA, CBAB, CCBA
Each case has 4!/2! = 12 arrangements.
So, there are 3 * 12 = 36 possible codes.
Thus, there are 36 different 4-letter codes that include all three letters A, B, and C.
