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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

User Mislav
by
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2 Answers

6 votes

Answer: b) 5040

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=(10!)/((10-4)!)=(10*9*8*7*6!)/(6!)\\\\=10*9*8*7=5040

Hence, the number of possible passwords formed = 5040.

User JaviAlgaba
by
7.5k points
4 votes

Answer: B) 5040

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

=
(10!)/((10-4)!)

=
(10!)/(6!)

=
(10* 9* 8* 7* 6!)/(6!)

= 10 × 9 × 8 × 7 = 5040

Thus, The required possible password is 5040.

User Npgall
by
8.6k points
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