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Standard XII

Mathematics

Combination with Restrictions

The total num...

Question

The total number of numbers of not more than $20$ digits that are formed by using the digits $0, 1, 2, 3$ and $4$ . is

5^{20}

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5^{20} - 1

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5^{20} + 1

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None of these

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Solution

The correct option is A $5^{20}$
Each of the place out of 20 ( $∵$ We can have maximum 20 digit number) has 5 possibilities. So, Total number of numbers
formed by $0, 1, 2, 3, 4$ are
$= 5 \times 5 \times \dots \times 5 (20 t i m e s) = 5^{20}$

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The total number of numbers of not more than $20$ digits that are formed by using the digits $0, 1, 2, 3$ and $4$ . is

The correct option is A $5^{20}$
Each of the place out of 20 ( $∵$ We can have maximum 20 digit number) has 5 possibilities. So, Total number of numbers
formed by $0, 1, 2, 3, 4$ are
$= 5 \times 5 \times \dots \times 5 (20 t i m e s) = 5^{20}$

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The total number of numbers of not more than 20 digits that are formed by using the digits 0,1,2,3 and 4. is

The correct option is A 520Each of the place out of 20 (∵ We can have maximum 20 digit number) has 5 possibilities. So, Total number of numbers formed by 0,1,2,3,4 are =5×5×⋯×5(20times)=520

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The total number of numbers of not more than $20$ digits that are formed by using the digits $0, 1, 2, 3$ and $4$ . is

The correct option is A $5^{20}$
Each of the place out of 20 ( $∵$ We can have maximum 20 digit number) has 5 possibilities. So, Total number of numbers
formed by $0, 1, 2, 3, 4$ are
$= 5 \times 5 \times \dots \times 5 (20 t i m e s) = 5^{20}$