Problem 2

Problem – 2

How many strings of five decimal digits

a) do not contain the same digit twice?

b) end with an even digit?

c) have exactly four digits that are 9s?

 

 

Solution:

a)      We have 10 digits to fill 5 places.

We can fill first place with 10 digits and second one with only 9 as repetition is not allowed and so on.

So number of strings of five decimal digits = 10x9x8x7x6 = 30240

 

b)      A number will be even if its last digit is 0,2,4,6,8

So we can fill last place of the string with 5 digits, and rest will 10 digits as repetition is allowed.

So number of strings = 10x10x10x10x5 = 50000

 

c)      When first digit is different than number of possible strings = 9

When second digit is different than number of strings = 9

Same for 3rd, 4th and 5th place,

So total number of strings = 9+9+9+9+9 = 45

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