Question

How many positive integers can be expressed ad a product of two or more of the prime numbers 5,7,11,and 13 if no one product is to include the same prime factor more than once?

Answer 1

11 positive integers can be expressed.

Explanation:

Consider the provided information.

The number of possible prime numbers are 5,7,11,and 13.

There are 4 possible prime numbers.

How many positive integers can be expressed as a product of two or more of the prime numbers, that means there can be product of two numbers, three number or four numbers.

The formula to calculate combinations is:
`^nC_r=(n!)/(r!(n-r)!)`

The number of ways are:

`^4C_2+^4C_3+^4C_4=(4!)/(2!(4-2)!)+(4!)/(3!(4-3)!)+(4!)/(4!)`

`^4C_2+^4C_3+^4C_4=(4!)/(2!2!)+(4!)/(3!)+1`

`^4C_2+^4C_3+^4C_4=6+4+1`

`^4C_2+^4C_3+^4C_4=11`

Hence, 11 positive integers can be expressed.