Question

13. Suppose in a certain state, all license plates have four letters {A,B,...Z} followed by three digits {0,1,2,...9). a. How many different license plates are possible? [2 points] b. How many license plates are possible in which all the letters and digits are distinct? (Distinct means no symbol is repeated). [3 points] c. How many license plates could begin with AB and have all letters and digits that are distinct? [3 points)

Answer 1

A, B, --- Yz Total - 26 letters 0, 1, 2, - - -,8,9 Total - 10 digits LDDD Lletten D-Digits No. of Combinations of letters (allowing Repetition) (26c,)(266) (366)(266) 26) No. of Combinations of Digits - (10 (,) (10 (1) (10 (1) = (10) Total no. of different liscence plates that are = 45,6976000 3 ye (21)9 (10) possible (b No. of Combination of letters (all are distinct) (266) 26/4c.)(23) - 26 x 25 x 24 x 23 3,5 8,800 No. of Combinations of digits = (10.,) (9c.) (8C) 10x9x8=720 Total mo. of listence plates Z. possible where all are distinct 658800) (120) 25,83,3 6,000

A B Remaining letters - 24 No. of Combinations of letters - 24P2 24x23 No. of Combinations of digits = 10 P3 = 552 101 = 10x9x8 71 =720 552 x 720 : Total no. of liscence plates that could begin with ABG rest are distinct symbols 3,97,440