Suppose that M is the product of k distinct primes. Find the number of ways to write N as the product of positive integers(>1), where the order of terms does not matter.(a) ^MCN-k(b) ^NCM(c) N * Bk(d) BkThis question was posed to me in unit test.Query is from Counting in section Counting of Discrete Mathematics

Suppose that M is the product of k distinct primes. Find the number of

1.	Suppose that M is the product of k distinct primes. Find the number of ways to write N as the product of positive integers(>1), where the order of terms does not matter.(a) ^MCN-k(b) ^NCM(c) N * Bk(d) BkThis question was posed to me in unit test.Query is from Counting in section Counting of Discrete Mathematics
Answer» Correct choice is (d) Bk The explanation: To solve the PROBLEM FIRST find the prime FACTORIZATION of each term of the product, and place the factors of each term into a box. Then, since N is the product of distinct prime factors, each prime factor appears in a unique box. Since the product of all of these terms is N, each prime factor must be in a box. Conversely, for any arrangement of these n distinct primes into r IDENTICAL boxes, multiply the primes in a box to create a term and the product of these terms results in N. This establishes the BIJECTION and the number of ways is Bk which is Bell number.

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