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

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: $^nC_r=\frac{n!}{r!(n-r)!}$

The number of ways are:

$^4C_2+^4C_3+^4C_4=\frac{4!}{2!(4-2)!}+\frac{4!}{3!(4-3)!}+\frac{4!}{4!}$

$^4C_2+^4C_3+^4C_4=\frac{4!}{2!2!}+\frac{4!}{3!}+1$

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

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

Hence, 11 positive integers can be expressed.