IAMRV wrote:

CAn anyone explain me how?

Positive integers can be expressed as a product of two or more of the prime numbers 5,7,11 & 13 if no one product is to include the same prime factor more than once.

We can say that a number can have all the 4 prime factors i.e. \(5 \times 7 \times 11 \times 13 =5005\).

This is 1 number.Now a number can be formed by 3 numbers i.e. we need to find to 3 numbers from 4 order of section is not important = \(\frac{4!}{3! \times 1!}= 4\) numbers. Also written as \(C^{4}_{1}\).

Similarly a number can be formed using only 2 primes i.e. we need to find to " numbers from 4 order of section is not important = \(\frac{4!}{2! \times 2!}= 6\) numbers. Also written as \(C^{4}_{2}\).

Hence summing all the 3 cases. \(6+4+1=11\)

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Sandy

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