A license plate in a certain state consists of 4 digits, not necessarily distinct, and 3...

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A license plate in a certain state consists of 4 digits, notnecessarily distinct, and 3 letters, also not necessarilydistinct.
(a) How many distinct license plates are possible if norestriction?
(b) How many distinct license plates are possible if it mustbegin and terminate by a digit?
(c) How many distinct license plates are possible if it mustbegin and terminate by a letter?
(d) How many distinct license plates are possible if the threeletters must appear next to each other?
(e) How many distinct palindrome license plates arepossible?
(A palindrome license plate is a license plate that reads the samefrom left to right as right to left)

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There are 10 different digits and 26 different letters a Each of the four digit can be filled in 10 ways and each of three letters can be filled in 26 ways Number of ways of selecting 4 places for digits out of 7 is C74 35 The possible number of different license plates is 35 See Answer

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