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iPad 14:13 *100% webassign.net Colgate Need Help? Read It Watch It 10. 1/3 points | Previous Answers WaneFMAC7 7.3.040 My Notes A certain identification number is a sequence of eight digits. (a) How many identification numbers are possible? 00000000numbers (b) How many of them begin with either 023 or 003? numbers (c) How many identification numbers are possible if no two adjacent digits are the same? (For example, 1234-5678 is permitted, but 1234-4567 is not.) numbers Need Help?Read It Submit Assignment Save Assignment Progress Home My Assignments WebAssign® 4.0 1997-2018 Advanced Instructional Systems, Inc. All rights reserved.Explanation / Answer
(a) All the 8 places can be filled with any of the 10 digits.
Thus, possible number of identification numbers = 10^8 = 100000000
(b) For numbers beginning with 023 and 003, only the remaining 5 places needs to be filled and each of these places can be filled with any of the 10 digits.
Thus, total such numbers = 2 × 10^5 = 200000
[2 is multiplied because numbers starting with 023 and 003 gives 10^5 numbers each]
(c) In these case, the first place can be filled with any of the 10 digits. The other 7 places each can be filled with any of the remaining 9 digits(except the one which is filled in the adjacent place)
Thus, total such numbers = 10 × 9^7 = 47829690 numbers
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