A learning software needs users.

A learning software needs an 8-digit password consisting of letters and numbers. Zhao uses the combination of four capital letters (not repeated) of D, E, F and W and four different non-zero numbers as his password, requiring the numbers to be placed in the last four digits, and the product of the four numbers must be a multiple of 320. So how many different possibilities are there for such a password?

A. less than 1000 species, B. 1000-3000 species, C.3000-8000 species and d. 8000 species or more.

Reference answer: b

Analysis: the first step is to investigate the problem of permutation and combination, and basically permutation and combination. In the second step, there are =24 possibilities for sorting the first four capital letters D, E, F and W.

The product of the last four digits is a multiple of 320. If it is one time of 320, it can be divided into 2× 4× 5× 8. If it is twice as much as 320, it cannot be divided into four different single digits to multiply; If it is three times that of 320, it can be divided into 4×5×6×8. Number of password types = 1 152. Therefore, choose option B.

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