The serial number on a bill consists of a letter followed by seven digits and then a letter. How many different serial numbers are possible, given the following conditions? (a) Letters and digits cannot be repeated. (b) Letters and digits can be repeated. (c) The letters are nonrepeated consonants and the digits can be repeated. (Let y be a consonant.)

Question

Mathematics

Evangeline Daniel

15 May, 19:42

The serial number on a bill consists of a letter followed by seven digits and then a letter. How many different serial numbers are possible, given the following conditions? (a) Letters and digits cannot be repeated. (b) Letters and digits can be repeated. (c) The letters are nonrepeated consonants and the digits can be repeated. (Let y be a consonant.)

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Answers (1)

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Benitez · Answer 1

408,844,800.

Step-by-step explanation:

(a) There are 26 letters in the alphabet and 10P7 ways of ordering 7 digits.

10P7 = 10!/3! = 604800

The answer is 26 * 604800 * 26

= 26^2 * 604800

= 408844800.