How many 5 digit numbers can be formed using the digits 1 2 3 if each digit is used at least once?

How many 5-digit prime numbers can be formed using the digits 1, 2, 3, 4, 5 if the repetition of digits is not allowed?

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NDA [Held On: 18 Apr 2021] Maths Previous Year paper

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1. 5
2. 4
3. 3
4. 0

Answer [Detailed Solution Below]

Option 4 : 0

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Electric charges and coulomb's law [Basic]

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Concept:

Prime number: Prime number are those which are divisible by itself and 1.

Calculation:

Not a single five-digit prime number can be formed using the digits 1, 2, 3, 4, 5[without repetition].

This is because if one adds the digits, the result obtained will be = 1 + 2 + 3 + 4 + 5 = 15 which is divisible by 3.

Hence, any number obtained as a permutation of these 5 digits will be at least divisible by 3 and cannot be a prime number.

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How many 5

How many even numbers of 5 digits can be formed with the digits 1,2 3 4 and 5?

How many numbers of up to 5 digits can be created using the digits 1,2 3 and 5 each at least once such that they are a multiple of 15?

How many number of 5 digits can be formed without repetition if I 2 3 and 5 always occur in each number II 0 never occurs?