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The question is from Permutation and Combination. Another question which combines number theory with combinatorics. Our task is to find number of 3 digits numbers which satisfies the given condition. This section hosts a number of questions which are on par with CAT questions in difficulty on CAT Permutation and Combination, and CAT Probability.

Question 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

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Explanatory Answer

Method of solving this CAT Question from Permutation and Combination: 3 digit number such that the product of their digits is less than 5

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.

The question is "Find 3 digit numbers such that product of their digits is a natural number less than 5?"

Hence the answer is "13"

Choice C is the correct answer.

 


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