1. (adapted from Ross, 1.1) California has a license plate system for cars (not
ID: 3351289 • Letter: 1
Question
1. (adapted from Ross, 1.1) California has a license plate system for cars (not including trucks) where the license plate consists of 7-places. The first place is a number; the next three places are letters; and the last three places are numbers (a) How many different California plates are possible? For example, a license plate may look different California plates are possible? For example, a license plate may loolk like 5C AA875. (b) How many different California plates are possible if we assume that no letter or number can be repeated i a single license plate? For example, a license plate may look like 5CAR893. 2. How many distinguishable letter arrangements can be made from the letters (a) UCSANTABARBARA (b) IHEARTCERSEILANNISTERExplanation / Answer
a) for first numebr there are 10 choices for next three letters 26*26*26 and for next three nmbers 10*10*10 choices are there as repetitions are allowed
hence total possible license plate =10*26*26*26*10*10*10=175760000
b) for repetitions are not allowed ; number of license plate =10*26*25*24*9*8*7=78624000
2)
a)total number of letters =14 which contains 1 U ; 1 C ; 1 S ; 5 A's ; 1 N ; 1 T ;2 B ; 2 R's
hence total numebr of arrangements =14!/(1!*1!*1!*5!*1!*1!*2!*2!) =181621440
b) total letters are 21 which contains ;3 I;s 1 H ; 4 E ; 2 A ; 3 R; 2 T ; 1 C; 2 S ; 1 L ; 2 N
hence total numebr of arrangements = 21!/(3!*1!*4!*2!*3!*2!*1!*2!*1!*2!) =3.69581*1015
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