Answer:
11 positive integers can be expressed.
Step-by-step 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: [tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
The number of ways are:
[tex]^4C_2+^4C_3+^4C_4=\frac{4!}{2!(4-2)!}+\frac{4!}{3!(4-3)!}+\frac{4!}{4!}[/tex]
[tex]^4C_2+^4C_3+^4C_4=\frac{4!}{2!2!}+\frac{4!}{3!}+1[/tex]
[tex]^4C_2+^4C_3+^4C_4=6+4+1[/tex]
[tex]^4C_2+^4C_3+^4C_4=11[/tex]
Hence, 11 positive integers can be expressed.
