Question

How many strings of length 6 over the alphabet {A, B, C} start with a C or end with a C?

Comments

$2\times 243-81=405 \ ?$

---

answer not given  @saxena0612  how you applied mutual exclusion plz explain detail

Answer 1

A =String starting with C of length 6 => 1*3*3*3*3*3 => 3^5

B = String ending with C of length 6 => 3*3*3*3*3*1 => 3^5

| A ∩ B | = String starting and ending with C of length 6 => 1*3*3*3*3*1 => 3^4

| A ∪ B | = | A | + | B | − | A ∩ B |

| A ∪ B |= 3^5+3^5-3^4

=> 2(3^5)-3^4

=> 3^4(6-1)

=> 3^4(5)

=> 81*5

405