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  • Calculate the number of ways two numbers can be chosen from the set of square of prime number up to 20 and multiplied together to obtain a product that is a multiple of neither 3 nor 6 nor 7.

Calculate the number of ways two numbers can be chosen from the set of square of prime number up to 20 and multiplied together to obtain a product that is a multiple of neither 3 nor 6 nor 7.

 

Option: 1

20


Option: 2

18


Option: 3

10


Option: 4

14


Answers (1)

To calculate the number of ways two numbers can be chosen from the set of squares of prime numbers up to 20 and multiplied together to obtain a product that is a multiple of neither 3, nor 6, nor 7, we need to identify the prime numbers and their squares within this range.

The prime numbers up to 20 are: 2, 3, 5, 7, 11, 13, 17, 19.

The squares of these prime numbers are: 4, 9, 25, 49, 121, 169, 289, 361.

Next, we need to determine the number of ways two numbers can be chosen from this set and multiplied together to obtain a product that is not a multiple of 3, 6, or 7.

The multiples of 3, 6, or 7: 9, 25, and 49 respectively. 

Therefore, we need to exclude these three numbers from our set.

The updated set of squares of prime numbers up to 20 is: 4, 121, 169, 289, 361.

To calculate the number of ways two numbers can be chosen from this set, we can use the formula for combinations: \mathrm{n C r=n ! /(r !(n-r) !)}.
The number of ways to choose 2 numbers from a set of size 5 is (5 choose 2) = 10 ways.

Thus, there are 10 ways to choose two numbers from the set of squares of prime numbers up to 20 and multiply them together to obtain a product that is not a multiple of 3, 6, or 7.

 

 

Posted by

Sumit Saini

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