# Questionbank: Permutation and Probability

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3 digit number such that the product of their digits is less than 5

## 3 Digit Number

Q.24: Find 3 digit numbers such that product of their digits is a natural number less than 5.
1. 11
2. 15
3. 13
4. 17

Choice C. 13

## Detailed Solution

For the product of a 3 digit number to be lesser than 5, it should comprise of either 1, 2 ,3 or 4 in a certain way.

Let’s start with product = 1 => this is possible in only one way (111).

Product =2 => Possible in 3 ways(211, 112 and 121).

Product = 3=> Possible in 3 ways(311, 113 and 131).

Product = 4 => Possible in 3 ways(411, 114, 141, 221, 212 and 122).

Total = 1+3+3+6 =13 numbers.

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