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?




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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