A website requires a four-digit numerical password in which the digits cannot repeat. How many possible passwords are there? . . A) 24. B) 5,040. C) 151,200. D) 3,628,801

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parmesanchilliwack parmesanchilliwack · Answer 1 · 2018-12-04T05:23:50-05:00

Answer: B) 5040

Step-by-step explanation:

Since total number of digits are 10 ( which are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

And, According to the question, website requires a four-digit numerical password in which the digits cannot repeat.

Therefore, required possible arrangement = \(10_P_4\)

=\(\frac{10!}{(10-4)!}\)

= \(\frac{10!}{6!}\)

= \(\frac{10\times 9\times 8\times 7\times 6!}{6!}\)

= 10 × 9 × 8 × 7 = 5040

Thus, The required possible password is 5040.

JeanaShupp JeanaShupp · Answer 2 · 2019-04-26T12:04:34-04:00

Answer: b) 5040

Step-by-step explanation:

Given: A website requires a four-digit numerical password in which the digits cannot repeat.

Total number of digits (0,1,2,3,4,5,6,7,8,9)=10

By permutation , the number of possible passwords is given by :-

\(^{10}P_4=\frac{10!}{(10-4)!}=\frac{10\times9\times8\times7\times6!}{6!}\\\\=10\times9\times8\times7=5040\)

Hence, the number of possible passwords formed = 5040.

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