Letters in a Name

Difficulty: Medium · Topics: Discrete Mathematics, Sets, Word Problems

In a class of 34 students, the number of students whose name contains the letters a and i at the same time is 10 less than the number of students whose name contains the letter a or the letter i , and 3 times the number of students whose name contains neither a nor i .

How many students have neither an a nor an i in their name?