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chetan2u
How many 4-digit number can be made from 2018 with repetition?

(A) \(4^4\)
(B) \(4^4-4\)
(C) \(4^4-4^2\)
(D) \(4^4-4^3\)
(E) \(4^3\)


Let's welcome 2018!!

Asked: How many 4-digit number can be made from 2018 with repetition?

Options for first digit = {2,1,8} = 3
Options for second digit = {2,0,1,8} = 4
Options for third digit = {2,0,1,8} = 4
Options for fourth digit = {2,0,1,8} = 4
Number of 4-digit numbers that can be made from {2,0,1,8} with repetition = \(3 * 4 * 4 * 4 = 4^3 (4-1) = 4^4 - 4^3\)

IMO D
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chetan2u
How many 4-digit number can be made from 2018 with repetition?

(A) \(4^4\)
(B) \(4^4-4\)
(C) \(4^4-4^2\)
(D) \(4^4-4^3\)
(E) \(4^3\)


Let's welcome 2018!!

we have \(4\) digits to choose from. But zero cannot be the first digit. Hence,

1st digit - \(3\) possibilities

Rest of the digits - \(4\) possibilities

\(3 * 4 * 4 * 4\)

\(3 * 4^3\)

\((4-1) * 4^3\)

\(4^4 - 4^3\)

Answer - D

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