How many ways arc there to arrange the letters a b c and d s

How many ways arc there to arrange the letters a. b, c, and d such that a is not followed immediately by b? What is the minimum numbers of students, each of whom comes from one of the 50 states, who must be enrolled in a university to guarantee, that there are at least 100 who come from the state? How many numbers must be selected from the set {I. 3, 5, 7, 9, 11, 13. 15 J to guarantee that at least one pair of these numbers add up to 16?

Solution

4 .

Answer:

4! ways to arrange a,b,c,d letters

a is not followed immediately by b then it is 3!

so total combinations are 4!-3! = 24 - 6 = 18 combinations