Question

4. How many permutations of the letters ABCDEFG contain: a) the string GD? b) the string AFC? c) the strings GD and AFC?

Answer 1

Solutimi. Given that The letters ABCDEFG cantain a we evaluate the string "GO" We know that de finition permutation Corder is important) P (n,r) - M! Definitim compinational order is not important) (mm) c (1,8) = (2) W with M1 = nin-) (1-2).... 2.). so we should use permutatims. we treat the men timed thus we have then the possible string as me single letter A, B, C, GD,E,F. We then letters which we want have to select 6 6 letters of letters. n=6 N= 6 evaluate the definition of a permutron: p(6, 6) = !! 1 ) 10) = 6! - 720

D we ewaluate the string 'AFC" The possible letters AFC,B,D,E, G. we then have 5 letters of which we want to select 5 letters. h-5 3- 5 evaluate the definition of a permutation. We get. P(5,5) = - = 5! =120. t-shi . I To we evaluate the string "GD" and "Afc" the possible letters AFC, GD,B E. We then have u letters. 4 letters of which we want to select n=4 8=4 evaluate the definition of a permutation we get plusu) = 9! (4-4)! p14, 4) = 4! P1414) = 41. | P14, 1) = 24